Notes

Review:

ABSTRACT: England in the seventeenth century was in the midst of turmoil: political, religious, and scientific. Civil war and regicide, puritan dissension, and a fundamental shift in the perception of nature all challenged the presumption of unity encoded in the notion of the harmony of the spheres. The very foundation of order and authority was at stake; but because the presumption of unity had prevented the development of a language of diversity, the historian has few sources for the transparent expression of conflict to mine for cultural meaning. The arts though are rich, albeit less than transparent, sources for investigating conflict; and because the harmony of the spheres was more than mere metaphor but perceived to be the very structure of the cosmos, seventeenth-century musical writing especially, both by well-known natural philosophers and by lesser-known musical theorists, encodes shifting notions of authority and order. These writers both created new musical theory and disputed theoretical issues, especially that of temperament tuning: the necessity to modify the heretofore perfect Pythagorean intervals to accommodate modern musical instruments and polyphony. In challenging the perfection of Pythagorean intervals and in claiming musical theory to be the provenance of human creation rather than of nature, musical writers were prognosticators unaware, trumpeting the shift to modernity as humanity wrested control of its destiny from the cosmos.

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IDEAS OF ORDER IN SEVENTEENTH-CENTURY MUSIC WRITING
Melanie K. Brooks-Nelson
B. A., University of Illinois, 1977
A thesis submitted to the
University of Colorado Denver
in partial fulfillment
of the requirements for the degree of
Master of Arts
History
2012

2012 by Melanie K. Brooks-Nelson
All rights reserved

This thesis for the Master of Arts Degree by
Melanie K. Brooks-Nelson
has been approved for the
Master of Arts in History
by
Carl Pletsch, Chair
Carl Pletsch, Advisor
Richard Smith
Gabriel Finkelstein
April 8, 2012

Brooks-Nelson, Melanie K. (M. A., History)
Ideas of Order in 17th-Century Music Writing
Thesis directed by Professor Carl Pletsch
ABSTRACT
England in the seventeenth century was in the midst of turmoil: political, religious,
and scientific. Civil war and regicide, puritan dissension, and a fundamental shift in
the perception of nature all challenged the presumption of unity encoded in the notion
of the harmony of the spheres. The very foundation of order and authority was at
stake; but because the presumption of unity had prevented the development of a
language of diversity, the historian has few sources for the transparent expression of
conflict to mine for cultural meaning. The arts though are rich, albeit less than
transparent, sources for investigating conflict; and because the harmony of the
spheres was more than mere metaphor but perceived to be the very structure of the
cosmos, seventeenth-century musical writing especially, both by well-known natural
philosophers and by lesser-known musical theorists, encodes shifting notions of
authority and order. These writers both created new musical theory and disputed
theoretical issues, especially that of temperament tuning: the necessity to modify the
heretofore perfect Pythagorean intervals to accommodate modern musical instruments
and polyphony. In challenging the perfection of Pythagorean intervals and in claiming
musical theory to be the provenance of human creation rather than of nature, musical
writers were prognosticators unaware, trumpeting the shift to modernity as humanity
wrested control of its destiny from the cosmos.
This abstract accurately represents the content of the candidates thesis. I recommend
its publication.
Carl Pletsch

ACKNOWLEDGEMENT
I wish to thank my advisor, Carl Pletsch, for insights that guided me to core issues in
my research.

TABLE OF CONTENTS
CHAPTER
1. INTRODUCTION..............................................1
2. CHANGING BELIEFS ABOUT NATURE AND MUSIC..................10
The Tuning Conundrum...................................11
Musics Place in Philosophy............................13
Four Early Philosophers on Music.......................16
3. MUSIC AND THE NEW PHILOSOPHY.............................20
Three Natural Philosophers on Music....................21
Bacon............................................21
Hooke............................................31
Newton...........................................36
4. HUMANITY CREATING ITS OWN MEANING........................39
Music Central to That Change...........................41
Changing Ideas of Nature in Music Writing..............42
5. THE NEW PHILOSOPHY: MUSIC AS SOURCE OF ORDER.............59
Acknowledging Diversity with Loss of Celestial Harmony.63
Continuing Religiosity With Philosophical Changes......65
6. CONCLUSION...............................................76
WORKS CITED.......................................................80
v

CHAPTER 1. INTRODUCTION
In the late sixteenth century, the Rosicrucian scholar Robert Fludd
diagrammed a Christianized concept of the Pythagorean monochord, the harmony of
the world in pictorial detail, displaying the musical order imposed by Goda
speculative, all-encompassing cosmological scheme. Calling it the Divine
Monochord, his detailed chart consists of two octaves, with internal intervals
designating hierarchical elements of the universe: earth, God, highest heaven.
Totally synthesizing macro- and microcosm was Fludds sensible and ambitious goal
in life.1 2 3 But his intricately constructed scheme amounted to the vain attempt of one
man to put together again the Humpty Dumpty fragments of science, philosophy,
and religion, which by then, on the cusp of the seventeenth century, had been
irrevocably sundered. Fludds was the final great flowering of speculative
music.
It was the Renaissance and it was modernity: divine right of kings and self-
governance; natural magic and natural philosophy; harmony of the spheres and the
silencing of the harmony; the great chain of being and the taxonomy of nature; Truth
and facts; mans place within a holistically organic nature and mans manipulation of
nature; music of numbers and music of sound; Pythagorean perfect intervals and
1 Anthony Aveni, Behind the Crystal Ball: Magic, Science, and the Occult from Antiquity Through the
New Age (New York: Times Books, 1996), 81.
2 Jamie James, The Music of the Spheres: Music, Science, and the Natural Order of the Universe (New
York: Copernicus, 1993), 128.
3 Joscelyn Godwin, Music, Mysticism, and Magic: A Science Book (London, New York: Routledge and
Kegan Paul, 1986), 143.
1

tempered tuning. Whatever one calls the transformation during the long seventeenth
centurythe Scientific Revolution writ large or smallEngland at the end of the
century was a world fundamentally changed from the England of the later sixteenth
century. The transformation, though, far from being linear or cumulative, was marked
rather by shifting and shared intellectual spaces, conflict and conflation, recession and
ascendance, anomaly and concordance. The philosophical debates that so consumed
thinkers and writers early on were left behind by the end of the period, not so much
resolved as peripheralized. The century was witness to an epistemological shift none
could have foreseen. The intellectual upheaval was defined by changing and
diversifying sources of authority in natural philosophy, politics, and religion. By the
end of the century, the notion of a harmonious cosmos had lost both its intellectual
bite and its cultural meaning as a shared perception of reality.
The first Stuart king of England, James I (James VI of Scotland), ruling after
Elizabeth from 1603-1625, continued her priority, formalized in the Elizabethan
Settlement, of maintaining harmony and a vision of unity within society, the via
media,4 treading a moderate path that rejected extremism in religion and politics and
elevated civil peace as the supreme good. The beginnings of a fundamental
breakdown in this harmonious perception of reality were evident in religion and
politics; and natural philosophers were already experimenting and exploring beyond
Renaissance frames of reference, rethinking assumptions about nature and the
cosmos. But both Elizabeth and James, through sheer force of powerful personae and
4 Alister McGrath, In the Beginning: The Story of the King James Bible and How It Changed a Nation,
and Language, and a Culture (New York, London, Toronto, Sydney, Auckland: Doubleday, 2001), 160.
2

ability to cajole, persuade, appease, and manipulate, were able to maintain the
appearance of unity and harmony, even as its breakdown was increasingly manifest in
natural philosophy, religion, and politics.
The rule of Charles I beginning in 1625 was not marked by the political ability
or force of personality of Elizabeth and James; he lacked the gifts to contain the
increasing fragmentation evident in society. His constant plying Parliament for more
funds, taking a Catholic bride, and choosing an archbishop widely perceived to be
much too cozy with Rome all served to raise the alarm of the people about the
maintenance of order. Where James had been able to placate and sustain the status
quo, Charles angered and, fatally, lost the trust of the people to rule for the common
good and to maintain order. The fall of the monarchy, regicide, and the interregnum
Commonwealth, far from being assaults on order, were attempts to restore order
within a society whose fear of chaos ranked almost equally with fear of eternal
damnation. Far from a clarion call for democracy, the condemnation of Charles and
turn to Parliament represented a desperate pursuit of an alternative source of unity
and order as monarchial disorder ran amok.
But unity, real or perceived, was never again to be. The mid-century break of
the Civil War and Commonwealth was more than political, more even than religious.
A changed society emerged from the grist of that mill, shocked at what had been
wrought in the beheading of a king,5 but never again to wholly trust king or
Parliament; agonizingly anxious to restore order and enforce civil conformity, but
5 McGrath, In the Beginning, 289.
3

forced to recognize fragmentation of authority in religion, politics, and natural
philosophy. The Restoration of the monarchy was not a return to former times, but a
new tacit agreement between people and king that the latter must accommodate the
former in new ways; William and Mary sailing into London in the Glorious
Revolution of 1688 made manifest the changed relationship between the people and
the monarchy.
That changed relationship was symptomatic of a shift throughout society, not
announced or articulated, and certainly not appreciated for the profound social and
cultural change it representednuanced and subtleyet utterly transformational.
Even as that shift permeated society, it entered into artistic products, representations
of shared cultural meanings. Art as ideological statement, that is, addressing notions
of order and authority, illuminates the changed epistemology from one of a unitary,
harmonious source of cosmological order expressed in the great chain of being and
the universal monochord to the recognition of diverse sources of authority; from the
notion of absolute Truth to acceptance of good-enough standards of truth; from God
as immanent in an organic, holistic nature to God the Creator existing outside His
Creation, a nature to be experimented on and manipulated by man.
Just as fundamental changes in natural philosophy were part of the
fragmentation of order and authority in politics and religion, so changing ideas about
the role of music in the cosmos and about basic assumptions in music theory were
embedded in the changing notions about nature and natural philosophy. Music was
identified with the harmony and order that structured all of society, an identification
4

that broke down as the reality of that harmonious unity in society broke apart and
music bifurcated into science and art, no longer the metaphysical glue of the cosmos.
Monumental as was the shift in musics role, it yet crept in like a thief in the night,
neither noticed nor noted, predicted nor understood, like the unheralded entrance of
the general epistemological shift of the century. No one willed what happened or
directed its occurrence; but by the end of the century, natural philosophy had become
merely science, and humanity bore the full weight of responsibility for the creation of
order and meaning in a cosmos devoid of both.
The central role of music in the shift to experimental science in the
seventeenth century it has been scantily studied in this connection. 6 7 8 Historians of
music concentrate on the history of method and performance practice, largely
irrespective of complex intellectual connections and currents of the century; and
historians of science have consigned music to the art category and thus not within
their purview. More broadly, music in relation to natural philosophy has not been
n
duly investigated. Historians have largely ignored the centrality of music in
o
structuring.. .knowledge and reality, an omission of the intellectual map of that
century.
6 Penelope Gouk, Music, Science, and Natural Magic in Seventeenth-Century England (New Haven and
London: Yale University Press, 1999), 19.
7 Jamie Kassler, The Beginning of the Modern Philosophy of Music in England (Aldershot, Hampshire,
England and Burlington, Vermont: Ashgate, 2004), 2; Linda Phyllis Austern, '"Tis Nature's Voice:
music, natural philosophy, and the hidden world in seventeenth-century England," in Music Theory
and Natural Order From the Renaissance to the Early Twentieth Century, eds. Suzanne Clark and
Alexander Rehding (Cambridge: Cambridge University Press, 2001), 31.
8 Paolo Gozza, ed., Preface, Number to Sound: The Musical Way to the Scientific Revolution
(Dordrecht, Boston, London: Kluwer Academic Publishers, 2000), xii.
5

Music writing of the seventeenth century is an integral part of cultural history
as a rich source of ideological statement in a matrix joining reality, representation,
and perception.9 Culture is implicit in constructing reality; cultural representations
embody and signify political codes and values,10 that is, notions of order and the
control of disorder. Musical writing is an important piece within the wide range of
cultural practices of the seventeenth century in addressing ideas of order;
investigating it helps redress its virtual omission in the centurys cultural topography.
About 100 treatises were produced in England in the long seventeenth century
(1580-1720), more than in any other place.11 12 Investigating these and other musical
writing is a sort of discourse analysis to reveal ideological meanings within cultural
practices, a way to examine questions of authority through these cultural
representations. These not only reflect prevailing ideas of order and authority, but
also inform and shape attitudes and beliefs: cultural discourse as ideological
legitimacy and context for political statement. This cultural turn in historical study
helps to avoid the pitfalls of imposed meanings, categories, and dichotomies in favor
of listening to contemporary sources own ideas of order and authority as expressed
through cultural products, an additional way to read the tumultuous events of the
12
seventeenth century.
9 Sharpe, Kevin, Remapping Early Modem England. Cambridge: Cambridge University Press, 2000,15.
10 Clifford Geertz, quoted in Sharpe, Remapping, 17.
11 Rebecca Herisonne, Music Theory in Seventeenth-Century England. Oxford: Oxford University Press,
2000, 6; Austern, '"Tis Nature's Voice," 31.
12 Sharpe, Remapping, 18-19.
6

Taking this cultural turn in intellectual history by reading musical writing has
resonance on another level for the seventeenth century. Musical writing as a cultural
expression has to do with order, not only in the general sense as in any historical
context; it also directly relates to the commonweal of the seventeenth century because
of a continuing and pervasive belief in correspondences and analogies through most
of the seventeenth century. These normatively depicted the cosmos as an
interconnected hierarchya representation, not a metaphorand writers of the time
were clear about the distinction. Truth on one level of meaning translated to truth in
13
another; this system of analogies was widely accepted and virtually unquestioned.
Music was identified with order through the harmony of the spheres and the universal
monochord. Order was the very fabric of the universe, expressed and organized by
music;13 14 and the tortuous route of the lost intellectual cache of this pervasive belief is
a critical piece of seventeenth-century intellectual history.
As part of its being a cultural representation of ideas of order and authority,
music occupies the same intellectual space as natural philosophy in the seventeenth
century, the former expressing identical notions of order and disorder, attitudes
toward nature and sources of authority as the latter. England was thrown into
epistemological ferment after papal authority was dethroned; writing about music is
one way to view the ensuing intellectual debates, political, religious, and
13 Sharpe, Remapping, 44.
14 James, Music of the Spheres, 3.
7

philosophical.15 The same network of practitioners of natural philosophy also wrote
about music in a speculative mode; that is, although they occasionally addressed
issues in musical theory, including the vexing one of tuning, they wrote more broadly
about the underlying mathematical and physical principles of music, beginning with
that iconic advocate of the experimental philosophy, Francis Bacon, and including
Hooke and Newton.16 Still, historians have been slow to appreciate the importance of
musical models.
Musical treatise writers in England, who seemed nearly obsessed with order in
their construction of a complex edifice of musical theory, incorporated the new
thinking about nature and order in their writing. Musical writing, like the New
Science in the seventeenth century, acted as a kind of code for imposing order; but the
code creators themselves were unaware of their role in the changing epistemology. To
this end, then, musical theorists both participated in and perpetuated new ways of
thinking of nature and music, even as they unselfconsciously continued alluding to
earlier Pythagorean musical notions of order and authority. Those writing about
music debated the urgent problem of tuningdivision of the scale, consonances, and
the proper nature of intervalsas well as more trivial ones: whether or not to attach
syllable names, in addition to letter names, to the notes of the scale; the optimal
number of lines on a staff; which note to assign to the bottom line of the staff. The
musical theory emerged in the context and as a reflection of epistemological change;
15 Ann Geneva, Astrology and the Seventeenth Century Mind: William Lilly and the Language of the
Stars (Manchester, New York: Manchester University Press, 1995), 40. She uses astrology as a similar
mapping device for the debates of that century.
16 Gouk, Music, Science, 3, 25.
8

so musical texts were sites of philosophical debate, albeit unconscious and non-
transparent.
The distinction between natural philosophers using musical models and
musical theorists writing about music, though, is a difference of intent. Both
addressed, in varying texts, changing ideas of music and music theory that were an
integral part of the more general intellectual ferment in natural philosophy.
Intellectual sites, then, for the new musical theory being threshed out were the same
ones as for the new experimental philosophy, embedded in changing notions of nature
and of sources of authority; and all musical writing of the seventeenth century,
experimental to practical, constitutes a single body of musical discourse mapping the
intellectual upheaval of the century. That the upheaval resulted in a foundational
philosophical shift by the end of the century was entirely an unintended consequence.
9

CHAPTER 2. CHANGING BELIEFS ABOUT NATURE AND MUSIC
These writers addressed not only the tuning problem but a range of issues
relating to music theory, creating most of the musical theory structure in place today.
Beliefs about nature inform music, always; and ideas about the natural order, though
having the gloss of immutability, are culturally determined. Music writing throughout
history attests to both its role as agent of change and its susceptibility to be changed
by culture. As ideas about nature change, so do ideas about music. Nature imposes
order on music theory, legitimizing it and providing authority for rules that, because
seemingly based on nature, appear to transcend culture and history. This illusion is
particularly salient for the shift from absolute Truth to scientific truth, reliable rather
than certain knowledge,* 18 19 in the seventeenth century. Even though truth was no
longer certain, the metaphysical search for it just did not matter anymore; reasonable
standards of truth about observable nature held sway. Importantly, though, as the new
natural philosophy narrowed into experimental science, abandoning any claim to
absolute Truth, it still retained its claim to universality, thus establishing its
hegemonic claim to knowledge in the modem era, epistemologically privileged
discourse.20
Just so, music morphed from a cosmological, mysterious, metaphysical
construct to a pursuit accessible and susceptible to scientific inquiry. Music was
Gozza, Introduction, Number to Sound, 29.
18 Clark and Rehding, Introduction, Music Theory, 2.
19 Karl Popper, quoted in Clark and Rehding, Music Theory, fn 5, 2.
20 Clark and Rehding, Introduction, Music Theory, 8.
10

contained and tamed, just as nature was in the seventeenth centurytransparent,
21
dissectible: from music as a divine force to music as a material phenomenon.
Music was linked with astronomy in the quadrivium and followed it from occult to
empirical investigation: from harmony of the spheres to disenchantment of the
world, a powerful metaphor for the cultural transformation wrought during the
seventeenth century and played out in music. The harmony of the spheres was
23
silenced in a world subjected to analysis and quantification.
Before the new science was legitimized, though, experiments were carried out
with some secrecy because of its association with natural magic. Only after the
Restoration and with the establishment of the Royal Society did experimental science
sufficiently separate itself from natural magic to be in the open. London became its
intellectual center, rather than the universities, because of the Royal Society; and
inhabiting the same intellectual spaces as experimental science, music became paired
24
with it, leaving behind its cosmological association with the harmony of the spheres.
The Tuning Conundrum
Musics move, with science, from the cosmological to the mundane universal
meant that it was now fair game for analysis and theoretical reworking, amenable to 22 23 24
Clark and Rehding, Introduction, Music Theory, 6.
22 This term was apparently coined by Friedrich Schiller and famously appropriated by Max Weber
and the Frankfurt School. In Clark and Rehding, Introduction, Music Theory, 6.
23 Gouk, Music, Science, 17.
24 Gouk, Music, Science, 54-55.
11

25
interrogation. Scientists and theorists writing about music argued vehemently
about a range of issues relating to music theory, none as central as the problem of
tuning. If one begins at the tonic or root note (do in any keys scale) and ascends or
descends in fifths or fourths or any other pre-determined interval, one will never
arrive precisely at the octave. Intervals of a fifth plus a fourth, for example, should
add up to an octave by Pythagorean reckoning; but they actually overshoot it by a bit.
Similarly, the twelfth perfect fifth and the seventh octave from the starting point
should culminate at the same point; but they do not. That specific discrepancy, the
tonal distance between the twelfth perfect fifth and the seventh octave, is the
definition of the Pythagorean comma, the core definition of the tuning problem.
Pythagorean perfect intervals are notperfect, that is. When music-making consisted
of a solo instrument or voice or a cappella music, this acoustical gap was not even
noted. But the advent of polyphonic music along with fretted and keyboard
instruments in the Renaissance inevitably led to the discovery of cracks in the crystal
spheres;25 26 accurate tuning was critical for fully exploiting the diatonic system.27
Equal temperament tuning simply subtracts a few oscillations from the
supposedly perfect intervals, a bit of fudging not discernable to the average listener,
to create twelve geometrically-derived equal semitones (each equal to the twelfth root
of two) that are, however, irrational numbers, very far in philosophical terms from the
supposed perfection of the arithmetic Pythagorean intervals: tuning rationality in
25 Daniel Chua," Vincenzo Galilei, modernity, and the division of nature," in Music Theory, Clark and
Rehding, 18.
26 James, Music of the Spheres, 87.
27 Clark and Rehding, Introduction, Music Theory, 6.
12

irrationality. These twelve tempered, irrational, half-tone intervals within the octave
now add up precisely to the octave interval, a seemingly straightforward,
uncomplicated solution. But with what cosmological significance that solution is
freighted; and this seemingly obvious resolution of the tuning problem became
standard practice only at the dawn of the nineteenth century.
Musics Place in Philosophy
Appreciating the seismic epistemological shift that equal temperament tuning
represents involves a corresponding appreciation of musics philosophical role
through the Renaissance. The ancient foundation of music was number, from the
Pythagoreans in the seventh to fifth centuries BCE. Making good music meant
choosing the right numbers: that is, creating consonances with perfect intervals.
These intervals were defined and illustrated by a monochord (invented by Pythagoras
himself, according to tradition), a single stretched string with a moveable bridge. The
octave, the most consonant interval, is sounded by placing the bridge at precisely the
middle of the monochord, creating a 1:2 ratio of total string length to compressed
length. The interval of a fifth, the next most perfect interval, is a ratio of 2:3, and the
fourth, the next most perfect after the fifth, is created with a 3:4 ratio. These intervals
were the most perfect, not primarily for the sweetness of their sound, but because the
13

integers used to form the ratios1, 2, 3, and 4were philosophically significant for
28
the Pythagoreans.
Pythagoreans conceived a precise universe, ordered by number, against the
materialistic universeearth, air, water, firethat was the focus of Aristotelian
natural philosophy. Aristotle, in thq Metaphysics, wrote of the Pythagoreans that they
believed mathematical principles, including musical ratios, to be the foundation of
everything, constituent elements of the whole of nature that were the ultimate reality.
For them, nature is of mathematics and music. The noted medieval music theoretician
Boethius (480-526) said that the Pythagoreans discovered the mathematical
foundation of musical consonances. (Boethius himself surmised that there must be
heavenly music because it was impossible to believe that the spheres could be moving
silently through the heavens. ) So the philosophical connection of music to nature
and number has very ancient roots.28 29 30
Music was identified with order, which was in turn identified with all of
nature and philosophy; order inhered in the universe, expressed and organized by
music, and was the very fabric and organizing principle of the universe. The universe
was seen as a totality, a unity; and all knowledge, morality, and purpose were
included in that. Man filled a meaningful and knowable, if lowly, niche in the
cosmological unity; his purpose for existence was intimately connected to the
28 The later medieval rationale for defining the fourth as dissonant was that, compared to the fifth,
which was reinforced because of consisting of two thirds, the fourth had no such theoretical
reinforcement. In Max Weber, The Rational and Social Foundations of Music, Trans, and ed. Don
Martindale, Johannes Riedel, and Gertrude Neuwirth (Carbondale: Southern Illinois University Press,
1958), 52.
29 Murray Schafer, TheTuning of the World (New York: Alfred A. Knopf, 1977), 260.
30 The format for this explanation is from Gozza, Number to Sound, Introduction, 1-4.
14

philosophical whole. The correspondence between earthly and heavenly music was
assumed, a manifestation of connected and communicating levels of reality. All
attempts at understanding nature were simultaneously attempts at finding mans
rightful place in the universe; the harmony of the cosmos and morality were
inextricable. Harmony, then, was more of a philosophical term than a musical one,
applicable to any level of reality or of nature because of the complex system of
correspondences and analogies that inhered in the universe. The universe was
perfectly tuned.
To suggest, then, that the perfect Pythagorean intervals were not perfect after
all was not merely to point out a mildly vexing issue requiring a technical fix, as the
problem might be framed today; it was to assault fundamental assumptions about the
universethe musical cosmos as the source of order, knowledge, and authority,
giving moral meaning to mans existenceand to undermine the very foundation of
Renaissance epistemology. The Renaissance view of the world, because it was so all-
encompassing, did not give way easily, quickly, or by a linear route. And although the
relentless onslaught of modernity in the seventeenth century has the certainty of
inevitability in hindsight, by no means would it have been viewed as such by the
centurys contemporaries. Rather, the intellectual habits and ingrained ways of
thinking about the cosmos only gradually lost intellectual cache as the new scientific
philosophy created new questions, priorities, and criteria to judge truth as it filled the
space left by gradually outmoded Renaissance thinking. 31
31 James, Music of the Spheres, 12.
15

Four Early Philosophers on Music
Robert Fludd and Johannes Kepler, Vincenzo Galilei and Zarlino, were on the
cusp of this change around the change of the seventeenth century but could hardly
have comprehended their pivotal place in intellectual history. Thinkers and writers
of a transitional period are disadvantaged by a rather murky sense of what they are
part of a transition to. For Fludd, the monochord so central to Pythagorean music-
as-number philosophy was more than a scientific instrument for defining and
measuring intervals; as we have seen in his Christianized rendering of the Divine
Monochord, it was also the scheme of the cosmos, the identification of the perfect
tuning of the universe. His was the last flowering of speculative music. Squarely
within the Renaissance tradition, Fludd was holding fast onto a world that was
beginning to cease to matter, obsessed with the kind of symbolic thinking that was
35
antithetical to the new philosophy.
Kepler, his contemporary and also an ardent Pythagorean-Platonist, is by
contrast, an intriguing watershed figure, one foot squarely in the Renaissance and one
in the new scientific epistemology; he heard the music of the spheres in full
polyphony, as a palpable symphony.32 33 34 35 36 Throughout his life, he immersed himself in
a range of intellectual passionsastronomy, astrology, theology, mathematics
32 Mary Campbell, Wonder and Science: Imagining Worlds in Early Modem Science (Ithaca and
London: Cornell University Press, 1999), 29.
33 Gozza, Introduction, Number to Sound, 4.
34 Godwin, Music, Mysticism, 105.
35 Keith Thomas, Man and the Natural World: Changing Attitudes in England 1500-1800 (Oxford, New
York: Oxford University Press, 1983), 67.
36 James, Music of the Spheres, 140.
16

believing ardently in a fundamental connection among them and making it his lifes
quest to discover it. Keplers approach was both speculativebeginning with an
assumption of the (polyphonic) harmony of the spheresand scientific: amassing a
wealth of data from his meticulous astronomical observations. Initially theorizing that
the planetary orbits could be precisely inscribed within a defined series of geometric
solids in a glorious Eureka moment, he subsequently found that the astronomical
data did not fit the theory. The scientist in him did not allow him to fudge the data,
but the speculative Renaissance man refused to abandon his assumption of cosmic
harmony. An ardent Christian, he believed that God must have created an alternative
scheme that Kepler simply needed to work harder to discover. What eventually
resulted, of course, were his laws of planetary motion, still valid today, a grand
synthesis of Renaissance and scientific epistemologies.
Vincenzo Galilei, father of Galileo and a generation before Fludd and Kepler,
was sufficiently independently minded and audacious to dare to expose the
imperfections in the Pythagorean intervals with simple experimental evidence and to
suggest a practical solution: tempered tuning. So he was the one to deliver the
opening salvo of the assault on Pythagorean perfection. His pronouncement came in
the context of a battle of words with fellow scholar and intellectual nemesis, Zarlino,
who argued strenuously against tempered tuning, insisting that singers instinctively
use just (non-tempered) intonation because it is from nature. Vincenzo scorned this
distinction, saying that no scale is intrinsically more natural than another. Although
17

he admitted that he found the just (untempered) fifth to be sweeter than the tempered
37 38
one, he personally knew many musicians who preferred the tempered fifth.
Vincenzos position regarding tuning was highly controversial because it
negated the idea of perfection in nature. Once that notion was dispensed with, the
entire edifice of the harmony of the spheres was suspect. Zarlino, contemptuous of
Vincenzo Galilei, still believed implicitly in heavenly harmony, perfection of nature,
order, and the unity of the cosmos. He vehemently rejected the skepticism of
Vincenzo, who contended that nature has no cognition, no intrinsic moral compass or
exemplary models; the old ideas of consonances and supposedly perfect ratios were
restrictive and incompatible with musical practicenot natural at all but a product of
human rationality. The aim of music, Vincenzo argued, was not to express perfection
but to communicate.
The debate between the two men was extremely heated, including vicious
personal attack: not surprising given that, although ostensibly debating the relative
merits of just versus tempered intonation, they were in fact striving against one
another about the nature of reality. Vincenzos stance was the first evidence of the
leading edge of the dispassionate view of musical philosophy and so of nature that
was to dominate the modem world. He did this in two ways: first, by objectifying
music as a field for experimentation and, second, by acting on this knowledge to 38 39
D. P. Walker, Studies in Musical Science in the Late Renaissance (London: the Warburg Institute,
University of London; Leiden: E. J. Brill, 1978), 19.
38 Walker, Studies, 113.
39 Chua, "Vincenzo Galilei," in Clark and Rehding, Music Theory, 17.
18

propose a modem system of equal temperament tuning.40 In pre-modern music, both
the cosmos and the soul are tuned to Pythagorean ratios, and earthly music is a
reflection of the celestial spheres. The cosmos is connected to earth by a monochord
(one detailed articulation of which was Fludds) linking the chain of being and
imposing unity and harmony. Music was the rational agent of enchantment. To
reject that enchanted role of music in structuring and giving meaning to the cosmos
was tantamount to untuning the cosmos.41 42 It is not an exaggeration, then, to say that
the contentious debate between Vincenzo Galilei and Zarlino was the turning point
42
of the Renaissance.
40 Chua,"Vincenzo Galilei," in Clark and Rehding, Music Theory, 23.
41 Chua,"Vincenzo Galilei," in Clark and Rehding, Music Theory, 22.
42 Gozza, Introduction, Number to Sound, 39-41.
19

CHAPTER 3. MUSIC AND THE NEW PHILOSOPHY
Through the ensuing century, the new experimental philosophy came into
ascendance, and music was central to the story, in two somewhat different senses.
First, as noted, music was identified with the structure of the universe in Renaissance
thinking; so any challenge to the central role of music in cosmology of was
tantamount to challenging epistemological beliefs. Second, with the growing
importance of polyphonic and instrumental music by the eve of the seventeenth
century, the tuning problem had to be addressed.
Because of its importance in the intellectual conversation of the time,
experimental natural philosophers devised experiments and wrote about music,
though usually not as an end in itself. These included Francis Bacon, at the beginning
of the century, Robert Hooke at mid-century, and Isaac Newton writing Principia and
his later unpublished scholia. The Royal Society, a gathering of gentlemen scholars
chartered by Charles II in 1660 and pledged to taking up the gauntlet thrown down by
Bacon to construct a new edifice of natural philosophy through experimental
investigation and observation, participated in the musical conversation by offering a
forum for discussion of musical experiments.
Aside from the well-known experimental philosophers, less noted musical
theorists wrote about music as a central concern, not as a way to elucidate other
scientific ideas or to explore the nature of sound. These (mostly) men created an
edifice of basic music theory that stands almost unchanged to this day, but also
engaged in protracted debates with proffered solutions for a range of musical issues,
20

including the tuning problem. These musical theorists were more narrowly focused
than the new natural philosophers who had only incidental interests in music. They
did, nonetheless, respond, think, and write within the same epistemologically shifting
milieu as the greater philosophers; and their musical writing, as an art product, is also
a source of illumination about that tumult.
Each offers hints about the complex, non-linear, even at times retrograde route
by which the new philosophy became epistemologically privileged discourse43 and
the way music figured in the grand conversation which was ultimately about sources
of authority and order. Musical writing illuminates challenges to the Renaissance
notions of the harmonic and moral structure of the cosmos and changing attitudes
toward nature: from an organic, unitary whole making up the Great Chain of Being
with humanity having its place in that continuum, to humans as the objective
observers of nature, experimenting and investigating to reveal its secrets.
Three Natural Philosophers on Music
Bacon
The name most firmly linked to the beginning of that is surely Francis Bacon,
and as such he warrants particular attention. Bacons early polemical tracts and the
longer, more fully-developed works of his later years set the agenda for early
experimental science and served as the methodological foundation of the Royal
Society after the Restoration. In a century marked by the coexistence of still-robust
43 Clark and Rehding, Introduction, Music Theory, 8.
21

Renaissance ideas alongside startlingly new philosophical notions, Bacons writing
stands as a metaphor for the creation of new intellectual spaces. His experimental
methodology is often cited as the hallmark of the revolution he helped lead; but his
project transcended mere methodology to initiate a repositioning of man in relation to
the cosmos and an alteration of the very foundation of order.
Had he foreseen the epistemological shift initiated by the new experimental
philosophy as it was to meet the powerfully fragmenting religious and political forces
of the century, Bacon may have given serious pause to his strident advocacy of his
philosophical agenda. He unquestioningly embraced Renaissance thinking even as he
advocated for the new philosophy. Natural magic, an experiment-based enterprise,
flourished along with scientific investigation in that century, with no clear distinction
made initially.44 Bacon himself was firmly planted in his own time, holding onto
ideas about nature and natural phenomena that would later appear scientifically
absurdideas which his own proposed methodology would help dismantle.45 He
unabashedly betrays magical Renaissance thinking even as he writes about his new
philosophy. In Sylva Sylvarum particularly, Bacon reveals the extent of his magical
and alchemical thinking, incorporating unselfconsciously an astonishing array of
magical beliefs into his explanations.46 Though heralded as scientific innovator and
44 Charles Webster, From Paracelsus to Newton: Magic and the Making of Modern Science
(Cambridge: Cambridge University Press, 1982), 2.
45 Richard Foster Jones, ed., Francis Bacon: Essays, Advancement of Learning, New Atlantis and Other
Pieces (New York: The Odyssey Press, 1937), xxviii.
46 Paolo Rossi, Francis Bacon: From Magic to Science, trans. Sacha Rabinovitch (Chicago: University of
Chicago Press, 1968), 12.
22

reformist, Bacon drew heavily on medieval and Renaissance traditions of natural
knowledge.47
Nevertheless, clear differences distinguish Renaissance natural magic and the
new natural philosophy, consigning the one to historical obscurity and the other to
philosophical dominance by the end of the century. The former focuses on the
unusual and the occult, promoting a sense of mystery, the latter on the ordinary and
revealed book of nature, striving for transparency and the resolution of mystery. Still,
because of the persistence of magical beliefs and natural magics experimental
methodology, the new philosophy (and Bacon, grudgingly) found common cause with
natural magic, the two coexisting in a shifting intellectual space for most of the
seventeenth century as natural magic gradually but inevitably lost intellectual cache
even as the new philosophy gained intellectual ascendancy.
While natural magic had its ascendancy in the Renaissance, Aristotelian
philosophy dominated the pre-Renaissance centuries; and Scholasticism continued to
be taught in the universities through the first part of the seventeenth century. Bacon
had only scorn for the failure of Aristotelian natural philosophy to actively investigate
nature to discover cause and effect and for relying instead on pointless argumentation
to no useful end. Aristotle is the Prince of Imposture.. .the Anti-Christ.. .who failed
to practice serious study and observation of natural phenomena, which are the only
Richard Serjeantson, "Natural Knowledge in The New Atlantis," in Francis Bacon's New Atlantis:
New Interdisciplinary Essays, ed. Bronwen Price (Manchester, New York: Manchester University
Press, 2002), 84.
23

48
basis of philosophy. Nature must be discovered through the (admittedly limited)
senses, aided by experimental method. Aristotelian rationalization is utterly fruitless
and does not produce discoveries, but.. .crushes and extinguishes them.* 49 For the
new experimental philosophy, Bacon envisions a marriage of nature and the rational
faculties, radically divorced in Aristotles philosophy. Let us establish a chaste and
lawful marriage between Mind and Nature... [that] from that marriage may issue
.. .wholesome and useful inventions... 50
Bacons contempt for Aristotelian philosophy and its intellectual handmaiden,
Scholasticismwords without actions, nature without investigation, talking without
doing51 52made Bacon hypothesis-shy. He insisted that the aim of his new philosophy
is the discovery of nature, not the construction of theoretical edifices. His idea of
reform for natural philosophy entails the construction of a complete natural history
from the active investigation of nature before any theory-construction. Bacons curt
dismissal of scholasticism and alchemythe one never faileth to multiply words and
the other ever faileth to multiply goldepitomizes his contempt. The role of
hypothesis in scientific investigation, now virtually unquestioned, was contentious in
the seventeenth century because of its connection to Aristotelian speculative natural
philosophy.
Francis Bacon, "The Refutation of Philosophies," in The Philosophy of Francis Bacon, ed. Benjamin
Farrington (Chicago: University of Chicago Press, 1964), 113,115.
49 Bacon, "Refutation," in Farrington, 125.
50 Bacon, "Refutation," in Farrington, 131.
51 Serjeantson, "Natural Knowledge," in Price, 85.
52 Bacon, Discourse in Praise of Knowledge, in Farrington, 15.
24

Scorn for Scholasticism, that complex, rationalist enterprise to reconcile the
teachings of the Church and Aristotle, prompted Bacon to insist on a rigid separation
of theology and philosophy. It was not a war between the two he fears, but rather an
unhealthy entwining of the two, such as had dominated Western philosophy and
53
theology for centuries. He saw this mingling of science and religion as pernicious.
Bacon continually emphasized the need to distinguish between Creator and Creation,
between God and nature. Failure to do so was a fatal flaw of the ancients in their
relationship with nature. Nature is evidence, but not the image, of God and must not
be reverenced. It is indifferent to humans; so humans must impose art on nature to
harness it for the good of humanity. Nature itself neither make[s] moral sense nor
exhibit[s] divine care.* 54 Mixing the two conflates and confuses the divine with the
natural and blurs the distinction between religion and science.55
Early on, Bacon presided over a firm separation of the new natural philosophy
from the religious enterprise, a bifurcation within natural philosophy, with all its
unresolved tensions, that has persevered to this day. Nonetheless, religion was the
primary concern of most people in the seventeenth century. So nature joined Scripture
as a new foundation of truth about God and the universe. Theories were reworked in
the language of the New Science. These reworkings were normative in the way the
old ones had been. New philosophers believed that investigation into nature would
confirm Scriptures veracity and thus bolster faith. The reformulations advocated not
Rossi, Francis Bacon, 97.
54 Jerry Weinberger, "On the Miracles in Bacon's New Atlantis," in Price, 117-118.
55 Rossi, Francis Bacon, 44.
25

a break with religion, but adding nature as another field of divine revelation in this
religious era.56 57 58 This framing of new science helped legitimize it and armor it against
accusations of atheism.
Still, the storm clouds of vague associations with atheism hovered
threateningly over the new philosophy; Bacon was prescient about the potentially
awesome power of technology bom of the manipulation of nature and believed that it
must be tempered with and guided by knowledge of God, a moral restraint he would
have assumed to be permanent and secure. He himself is uncertainly suspended
between atomismmaterialistic but with the taint of atheismand Stoical theory of
pneumauncomfortably close to reintroducing divinity into nature, philosophically
untenable. But the cautionary religiosity Bacon saw as a permanent part of this re-
alignment was eroded and eventually destroyed by his own methodology; and so too
notions of order became severed from morality and religion to become strictly
human-fashioned. Regardless of Bacons own misgivings, the notion of an inert
nature with the rejection of God immanent in nature set the agenda for the
seventeenth century and is intimately linked to evolving concepts of order and
authority. Bacon continually emphasizes the necessity of distinguishing between the
58
Creator and His Creation and natures moral indifference.
56 Roy Porter, "Creation and Credence: The Career of Theories of the Earth in Britain, 1600-1820," in
Natural Order: Historical Studies of Scientific Culture, eds. Barry Barnes and Steven Shapin (Thousand
Oaks: SAGE Publications, 1979), 98.
57 Weinberger, "Miracles," in Price, 115.
58 Weinberger, "Miracles," in Price, 117-118. Also, early modern science was almost entirely a male
pursuit. The fact that medieval institutions, most notably the hegemonic Church, were the exclusive
realm of men meant that the institutions that grew out of that tradition continued to be dominated
by males. Because of the clerical origins of early modern science, the "conceptual and ideological
26

In music this meant a movement away from music as number to music as
sound. Bacon stoutly rejects the notion of the harmony of the spheres and Platonic
ratios as the foundation of the cosmos. Since physical, not mathematical,
investigation of the universe is his aim, music is a sensible acoustic event, not a
source of mathematical speculations. This Platonic rejection, ironically, mimics
Aristotle, who also rejected philosophical notions of cosmic harmony. Both Aristotle
and Bacon, though, adhered to other Platonic ideas including a universe based on
order and proportion and a belief in the moral and emotional power of music.59
Bacons approach to music and sound, in fact, incorporates natural magic as
well as experimental philosophy. He thinks music can be used for utopian ends
through science and technology and is the first to propose a program for the empirical
investigation of sound through a mix of observation, imitation and manipulation of
nature,60 detailed in Salomons House in The New Atlantis. This work draws heavily
on medieval and Renaissance traditions of natural knowledge.61 Though its setting
is fantastical, Bacon insists this work is not a utopian vision but rather a realizable
goal for a society properly employing technology for the good of humanity.62 The
paragraph on sound-houses describes a magical-technological approach to
investigation:
structure" of medieval institutions remained intact regarding gender roles. Bacon strove to break the
fetters of traditional Aristotelian philosophy; challenging gender roles too would likely have been
beyond his ability to comprehend. In Revolutionizing the Sciences: European Knowledge and Its
Ambitions, 1500-1700, Peter Dear (Princeton, NJ: Princeton University Press, 2001), 16.
59 Gouk, "Music in Francis Bacon's Natural Philosophy," in Gozza, 136.
60 Gouk, "Music," in Gozza, 137.
61 Richard Serjeantson, "Natural Knowledge" in Price, 84.
62 James Spedding, Preface to The New Atlantis, in The Works of Francis Bacon, Vol. V, eds. James
Spedding, Robert Leslie Ellis, and Douglas Denon Heath (New York: Houghton Mifflin, 1904), 351.
27

We have also sound houses, where we practice and demonstrate all
sounds and their generation. We have harmonies... .Diverse
instruments of music... .We represent small sounds as great and deep;
likewise great sounds extenuate and sharp; we make divers trembling
and warbling of sounds... .We represent and imitate all articulate
sounds and letters, and the voices and notes of beasts and birds. We
have certain helps which set to the ear do further the hearing greatly.
We have also divers strange and artificial echos, reflecting the voice
many times... .We have also means to convey sounds in trunks and
pipes, in strange lines.63
Bacon writes more generally about music as part of his plan for the new
natural philosophy. In Sylva Sylvarum, divided into ten centuries, each containing 100
experiments, Century II focuses on music. The introductory paragraph is the most
famous of Bacons observations on music:
Music, in the practice, hath been well pursued, and in good variety; but
in the theory, and especially in the yielding of the causes of the
practique, very weakly; being reduced into certain mystical subtilties,
of no use and not much truth. We shall, therefore, after our manner,
join the contemplative and active part together.64
Bacon has little use for the elaborate structure of Renaissance music theory,
based on Pythagorean intervals and mystical number relationships. As in all of his
natural philosophy, he wants to investigate the causesof musical sound, in this case.
He agrees with theorists that the octave is the most consonant intervalThe
diapason or eighth in music is the sweetest concordbut says the cause is dark,
and hath not been rendered by any.* 65 Bacon, who ostensibly seems perverse in
claiming ignorance in his Sylva Sylvarum of the octave-unison relationship, for
Bacon, Works, Vol. V, 407.
Francis Bacon, Sylva Sylvarum, "Century II," in Works, Vol. IV, 225.
Bacon, Sylva Sylvarum, in Works, Vol. IV, 226.
28

example, since the foundation for Platonic intervals was well-known,66 is actually
merely admitting he does not know about the connection between frequency of
vibration and pitch, a discovery just making its appearance on the intellectual
horizon.67 He goes on to suggest it must be that the air is forced into a regular pattern
to give the sweet sound of the octave.68 In the matter of the two half-tones of the
major scale, Bacon says the varying is natural... required by nature.69 70 So much for
causes.
Bacon agrees with Renaissance theorists in the order of the sweetness of
interval consonances, except about the interval of the fourth. The question of the
consonance of this interval was much debated, but composers of polyphonic music
needed it and were using it freely. Bacon favors the fourth as consonant, claiming
accord with ancient tradition. The concords in music which are perfect... are the
fifth.. .the third.. .the sixth... and, as the ancients esteemed, and so do myself and
some other yet, the fourth, which they call the diatessaron. This is the pragmatic
stance, admitting what was already virtually standard in musical practice.
Study of consonances was of paramount concern to Bacon, as to every writer
on music in the seventeenth century. In an intriguing discussion about the causes of
sweetness of sound, Bacon makes an analogy with sight. There be two things
pleasing to the sight. ..colours and order The pleasure of color is analogous to the
66 Walker, Studies, 120.
67 Gouk. Music, Science, 167.
68 Bacon, Sylva, in Works, Vol. IV, 227.
69 Bacon, Sylva, in Works, Vol. IV, 227-228.
70 Bacon, Sylva, in Works, Vol. IV, 228.
29

sweetness of a single tone, but the pleasure of order doth symbolise with harmony.
Garden knots, good proportion, and symmetrical figures please; while irregular
shapes are deformities. Harmony equals beauty equals order. Order is loved, even
revered, all the more so as the desperate hope of an early-seventeenth-century society
seeming to be losing its unitary way amidst religious and political divisions. But to
find the proportion of that correspondence [harmony], is more abstruse, an
inquiry for another day, apparently, as Bacon does not investigate causes of harmony
in Sylva Sylvarum.
He addresses the issue of musical sound though, describing experiments with
various materials and instruments to produce a variety of pitches but omitting,
interestingly, any reference to the monochord. He is either ignorant of it or thinks,
perhaps, the reference touches too closely on mystical Pythagorean number intervals.
The intervening and concluding observations describe the creation and transmission
of sound and its connection with the percussion of air and vibration. A seemingly
glaring omission is any discussion of the tuning problem, becoming acute because of
the prevalence of both polyphonic music and fretted and keyboard instruments.
Instead, Bacons century on music, though freely drawing on other sources as does all
of Sylva Sylvarum, focuses on finding causes for observed phenomena through
experimentation.
Bacon, Sylva, in Works, Vol. IV, 229-230.
Bacon, Sylva, in Works, Vol. IV, 230.
Bacon, Sylva, in Works, Vol. IV, 257-261.
30

In disentangling Aristotelian philosophy from Christianity, Bacon unwittingly
aided and abetted the sowing of the seeds of secularization by participating in the
fragmentation of authority begun with the Protestant reformation. It is an outcome
Bacon himself would have stridently condemned. Others through the century
participated in the subordination of mystical Platonic and Pythagorean philosophy in
favor of scientific knowledge as the criterion for authority; virtually all of them too
would have strenuously decried the materialistic, secularizing consequences of that
action. And that is the ironic story of early modernity: the fragmentation of sources of
authority and order, borne of an altered relationship to nature and sincere religious
sentiment.
Hooke
Later in the century, Robert Hooke was the consummate experimental
investigator. As Robert Boyles assistant in the 1650s (pre-Royal Society), he devised
mechanisms for conducting Boyles own experiments. The most famous was, of
course, the air pump, later to become a mainstay of Royal Society discussions and
experimentation. His enthusiasm for experimentation was recognized by the Royal
Society, which named him the first Curator of Experiments and later Secretary of the
Society after Oldenburgs death in 1677. In his experimental mode, Hooke relied on
hypothesis-testing, drawing sharp criticism from Newton, who saw this methodology
as anti-empirical, muddying the waters by proposing imaginary, contrary
explanations for natural phenomena already confirmed by experiment and
31

74
observation. Hooke in turn upbraided Newton for his (Newtons) dogmatism in
stating with absolute certainty, for example, that he had proved his theory of optics
75
and proposing his own alternate hypothesis for the data.
But far from being a dilettante, Hooke was an ingenious tinkerer, finding
creative solutions to practical problems.* 75 76 77 78 79 Even though he advocated a mathematical
approach to the development of natural philosophy, his forte was inventing devices to
further the cause of useful experimentation. He helped advance the field of
microscopy for his magnum opus, Micrographia (1665), one of the few books
published under the auspices of the Royal Society. Also, Hooke found that he
required a better light source than a simple candle or lamp to properly enhance the
image from the microscope. His answerthe sotoscope, a liquid-filled glass globe
placed between light source and microscope and focused with a convex lens to direct
the intensified light on to the specimen. Hooke was not unaware of his creative
gifts. On more than one occasion, he claimed to have found a clock-based solution to
that Holy Grail of seventeenth-century science, the longitude problem. While
acknowledging that the senses were prone to narrowness and wandering, he had
Peter B. Anstey, "Experimental Versus Speculative Natural Philosophy," in The Science of Nature:
Patterns of Change in Early Modern Natural Philosophy, eds. Peter Anstey and John A. Schuster (The
Netherlands: Dordrecht, 2005), 229, 232.
75 Steven Shapin, The Scientific Revolution (Chicago: University of Chicago Press, 1998), 115-116.
76 Marcus Hellyer, The Scientific Revolution (Oxford: Blackwell Publishing, Ltd, 2003), 195. Hellyer
maintains that twentieth-century historians of the scientific revolution fail to appreciate the extent to
which seventeenth-century natural philosophers pursued science to solve practical problems.
77 Hellyer, Scientific Revolution, 180-181.
78 Lisa Jardin, Ingenious Pursuits: Building the Scientific Revolution (New York: Random House, Inc.,
1999), 44.
79 Jardin, Ingenious, 51. It was not until the latter part of the eighteenth century that John Harrison
found a clock-based solution to that vexing problem of navigation. In Longitude, Dava Sobel
(Middlesex, England: Penguin Books, Ltd., 1996).
32

confidence that instruments such as the microscope and telescope would adequately
compensate for these shortcomings. 80 81 82 83
Hooke thought about more than experiments, though. He believed that the
ancients possessed great philosophical truth, but that it had become severely
compromised over time. It is said of great Empires, that the best way to preserve
them from decay, is to bring them back to the first Principles... on which they did
begin. The same is undoubtedly true in Philosophy. Like most other natural
philosophers of the time, Hooke professed a personal godliness and religiosity. Under
his microscope lens, he saw revealed such perfect adaptation between structure and
function that he wondered how anyone could think all those things the production of
chance. Also coincident with most of his peers in natural philosophy, Hooke
believed the purpose of natural philosophical knowledge was to erect a glorious and
83
everlasting structure to nature and thus natures Creator.
Musical investigation constituted an important part of Hookes experimental
agenda, mostly relating to the nature of sound, ranging from vibrations and acoustics
to the nature of harmonious intervals and the effects of music. He understood sound
as vibration and, more importantly, related frequency to pitch in his experiments.
Most of Hookes musical experiments were presented to the Royal Society in 1664.
In addition to the experiments presented to the Royal Society, Hooke presented
papers focused more on the effects of music to a secret Philosophical Club, formed in
80 Shapin, Scientific Revolution, 93.
81 Hooke, quoted in Shapin, Scientific Revolution, 75.
82 Hooke, quoted in Shapin, Scientific Revolution, 144.
83 Hooke, quoted in Shapin, Scientific Revolution, 153.
33

the mid-1670s by Hooke and others, including Christopher Wren and William
Holder, interested in musical topics. In papers probably prepared for this group,
Hooke hypothesized that nature has constructed the ear to receive sound exactly as it
is produced, that is, in the same frequency. The consonant intervals (octave, fifth,
fourth, etc.) are pleasing and harmonious, not because of mystical Pythagorean
numbers, but because these are the frequencies that strike the ear in a coincidence of
the Vibrations. Rhythm is that which is most active and operative upon the
affections & passions of men. Harmony, though, offers the most ravishing pleasure
& delight of all. It is an intellectual pleasure because the mind must sort out the
mathematical intricacies of the music to make it pleasurable. This is possible because
God has created both the world and humans according to mathematical, geometric
principles.84 85
Hooke, along with Newton, saw music as the underlying structure of the
universe,86 87 an idea that seemed to peacefully co-exist with his cutting-edge
experimentation on vibration theory. He constructed musical models, not primarily to
explain musical principles, but to elucidate his natural philosophy in the context of
this larger notion of the harmonic structure of the universe, with mathematics as the
connecting vector. This notion is, of course, essentially Pythagorean; and Hooke
unabashedly subscribed to this Renaissance idea to design experiments and create
84 Hooke, "Curious Dissertation concerning the Causes of the Powers and Effects of Music," in Gouk,
Music, Science, 200 and 207-209. Hooke also prepared a series of "Musick Scripts" to discuss his
ideas, likely for the Philosophical Club.
85 Hooke, "Curious," in Gouk, Music, Science, 212-213.
86 Gouk, Music, Science, 225.
87 Gouk, Music, Science, 213.
34

explanations: music as a means to an end rather than an end in itself. Most notably, he
compared the minute particles constituting matter to the action of vibrating strings to
explain the nature of matter and conducted experiments in acoustics and musical
vibration to articulate and fortify his own theory of vibrating matter. Again, he used
musical analogies when detailing his theory of color by comparing the spectrum to
89
musical harmonies and his notion of light by comparison to sound waves.
Hooke also weighed in on musical issues in their own right, including musical
notation and division of the scale. His approach was, typically, a combination of
Pythagorean mysticism and experimental practicality, his ideas on these matters
based on widely held ideas of the time, not original but rather his own unique
presentation. Whether to give names to the twelve tones of the octave and what those
names should be was one much-discussed (though hardly pivotal) musical issue of the
time. Hooke suggested a system of musical notation as an attempt to simplify and
rationalize both reading and composing music. The division of the scale, an issue
closely touching on the tuning conundrum, pre-occupied mathematicians and
theorists; and it is clear that Hooke was aware of others geometrical and irrational-
number calculations for the scale divisions. Though acknowledging the necessity of
some kind of temperament tuning for practical musical production, Hooke never went
so far in musical theorizing as to offer any solution of his own devising; and he 88 89
88 Gouk, Music, Science, 214, 218.
89 Gouk, Music, Science, 201, 216.
35

maintained that the true intervals were of just intonation (Pythagorean plus additional
consonant intervals advocated by Zarlino).90
Newton
Much greater even than Hooke, Newton wrote that masterwork of Western
mathematical logic, Prinicipia mathematica (1687), but was loath to publish it. His
friend Edmund Halley persuaded him to do so by paying for its publication under the
auspices of the Royal Society.91 92 93 Newton was a serious investigator of alchemy and
considered his alchemical studies to be the core of his lifes work. His volumes of
writing mostly concern his astrological and alchemical investigations and
speculations; and his personal library included mostly books on these subjects and
92
only a few on the new scientific philosophy.
The initial work on Prinicipia mathematica (1687), as well as Newtons
discovery of the law of gravity, was a product of his anno mirabilis, the year Newton
spent at home when Cambridge was closed for fear of the plague. Newton, though,
saw both of these scientific-mathematical accomplishments in terms of their value in
penetrating the meaning of Pythagoras celestial harmony; the Pythagorean musical
ratios underlay his inverse square law. According to Newtons scholia, both the
inverse square law and the law of gravity were adumbrated by the prisci theologi in
90 Gouk, Music, Science, 201.
91 The Royal Society, however, lacked the funds to repay Halley, so recompensed him with multiple
copies of Francis Willoughby's Historic! piscium, a lavishly illustrated non-seller published by the
Society the year before. In Ingenious, Jardine, 36.
92 James, Music of the Spheres, 160.
93 Gozza, Number to Sound, 50.
36

the mists of antiquity.94 This consummate man of science and mathematics, the very
epitome of seventeenth-century brilliance, viewed his monumental intellectual
creations as mere re-interpretations of ancient encoded wisdom.
Not surprisingly, Newtons interest in music was based on mathematics. He
developed his own system for the division of the scale, a task exercising theorists
mightily because of its intimate connection with the tuning problem. Newton devised
a chart of logarithmically calculated tempered semitones that anticipates almost
precisely that in use today.95 He seems more interested in the mathematical
complexities and creating symmetry than in aural considerations; and he is anxious to
construct a system of intervals, by theorizing tiny building blocks of sound, that is
closest to classical just intonation. Newtons musical theorizing is a part of his
obsession with mystical number manipulation relating to ancient wisdom rather than
a desire to derive some practical solution for the temperament problem facing
practicing musicians. He used his acoustical work to inform his optical investigations,
drawing an analogy (as others also did) between the musical scale and the color
spectrum.96
Newton, following Pythagoras, believed the cosmos to be structured by
mathematics, evident in Principia, and himself as an agent to recover ancient
theological wisdom. His investigation into the harmonics of both music and color was
part of his lifelong attempt to reveal the true basis of the harmony of the spheres, the
94 Walker, Studies, 25.
95 Gouk, Music, Science, 233.
96 Gouk, Music, Science, 235, 237.
37

truth of which had been encoded to hide it from the vulgar but symbolically and
allegorically decipherable by a true philosopher such as Newton himself. The musical
scale and the color spectrum relate to the actual harmony of the heavens, not the
literal creation of tones by the motion of crystal spheres, but the entire mathematical
edifice underlying the cosmos. Newton saw himself, not as a discoverer of new
truths about the working of the universe, but as one revealing its ancient, encoded
98
wisdom. Absolute space was, to Newton, Gods universal sensorium. 98
Gouk, Music, Science, 251-254.
98 Peter Dear, Revolutionizing the Sciences: European Knowledge and Its Ambitions, 15001700
(Princeton, NJ: Princeton University Press, 2001), 169.
38

CHAPTER 4. HUMANITY CREATING ITS OWN MEANING
Implicit within the centurys changing perspectives on nature as they inform
altered sources of authority and order is the notion that humans now have chosen to
make do for themselves. The cosmos is delineated, humanity is in the ascendant,
nature is knowable and controllablea pyrrhic victory, exacted at the cost of the
severing of once-vital connections: between nature and morality, meaning and spirit,
science and philosophy. Humanitys pride in its newfound control of nature and
authority, wresting power from a spiritually imbued cosmos to bring to earth as its
own provenance, wraps the onus in the guise of a gift of increasing scientific
hegemony. From now on, humankind itself must operate without reference to the
harmony of the spheres. If there is to be harmony, humanity must be both originator
and guarantor. On its own in the cosmos, no longer part of a great chain of being
ensconced within a unique niche of the natural world, no longer dependent on a
shared notion of cosmic harmony, rather relying on its own power to create and
sustain, to order and deliver, to provide and satisfyhumanity is the ultimate source
for all its own physical, intellectual, and spiritual needs.
One initially compelling metaphor maintains that the traditional religious
ideology underlying the new theory of nature in the seventeenth century is the basso
continuo, supporting the status quo; new lyrics and melody are the changes in
39

philosophy and religion that play over it." But the basso continuo was not left
unchanged, even if the moral-religious ethos remained strong. Though not apparent
early in the seventeenth century, the moral and the religious were destined to be only
vestiges, however sincerely proclaimed, that eventually revealed their uselessness to
the new natural philosophy; the new basso continuo is the modern scientific
enterprise: materialistic, radically divorced from religion, ideologically neutral. The
source of morality, religion, and ideology no longer lies with the cosmos; humans
now have the freedom, or bear the burden, of fashioning these anewfor each
individual and for society. It is a human-made world, in much more than a merely
technological sense. This new way of thinking about nature was part of a deep and
wide shift within societypolitical, philosophical, and religiousrecognizing that
humanity, without recourse to the immutable heavens, must now be in control of its
own destiny, including the awful freedom to choose among diverse sources of
authority and order.
This new natural philosophy was not just about changing methodology. New
ideas about nature and mans relationship to it redefine order and authority, a true
epistemological shift. But in no sense was it a linear one. Renaissance-era beliefs in
analogies and correspondences continued to be culturally meaningful even as the
scientific revolution proceeded apace. This contradictory, complex seismic shift can
be viewed through artistic products as they reveal, though opaquely,* 100 prevailing
Porter, "Creation and Credence," in Barnes and Shapin, Natural Order, 101.
100 Sharpe, Remapping, 40.
40

beliefs, concerns, and desires, expressing illusions as well as anxieties.101 102 103 Reading
cultural texts for ideological meaning is critical for the seventeenth century in
particular because political thought and language did not even exist as a distinct,
discrete level of discourse until the latter part of the century and because the
participants in the profound shift of cultural meanings in the seventeenth century were
utterly unaware of the transformational enterprise of which they were a part. So the
upheavals of the seventeenth century, far from being transparently expressed in
cultural products, often led to a forceful articulation of organic unity as writers
agonized about their fear of disorder in the face of disintegrating certainties or, later
in the century, more easily embraced the new epistemology identified by
fragmentation of sources of authority and truth as old meanings and attachments
mattered less and less.
Music Central to That Change
Music figures critically in this epic shift in having become, through evolution,
hard-wired into the human brain, a source of social cohesion since humanitys pre-
history. All known societies have had music; it is intimately connected with the
development of language, dating to the beginning of our species.104 Music is central
to what it means to be human; so the musical conversation of the seventeenth century
is even more heavily freighted with meaning than just one among any number of
101 Sharpe, Remapping, 29.
102 Sharpe, Remapping, 48.
103 Sharpe, Remapping, 49.
104 Oliver Sacks, Musicophilia (New York: Random House, Inc., 2007), x.
41

other cultural expressions as political statements. Musical writing, however narrowly
focused, is yet accessing a deep human reservoir of meaning of sources of order and
authority. As humans assumed increasing autonomy, this epic shift is encoded in
music thinking and writing.
Changing Ideas of Nature in Music Writing
That dividing line of seventeenth-century English history, the Civil War, was
a cultural break in forcing the polity to confront the fact of fragmentation and loss of
harmony; but it was not the cause or even the symptom of a sharp break in that belief
in a unified and harmonic society. That had been eroding for some time, as evidenced
in the temperament controversy in music. The realization that there was a problem
with the intervals as pronounced by Pythagoras was known by those who worked in
music; and with that realization came inevitable enormous cosmological implications:
the harmony of the spheres was not as advertised. As musical theorists and
practitioners grappled with the temperament problem, the out-of-sync intervals
pointed to more questions, and questioning, about other accepted truths concerning
the physical universethe great chain of being and mans niche within italong
with more mundane but pressing matters of politics and society.
The new realizations and realities in society and philosophy meant that
humankind was severing its spiritual ties to nature and cosmos, arrogating to itself the
roles previously belonging to a sacralized universe, thus desacralizing those functions
as they came within the realm of human-created control and authority. Though
42

musical treatise writers reveal an increasing sense of mastery as well as continuing
anxiety about shifting cosmology through the century, the changes are highly
contested and non-linear.
The Royal Society tended to attract men (and only men of course) with a
range of interests pertaining to the new experimental philosophy, including music as a
means of elucidating other ideas and occasionally musical topics per se. Musical
theorists were not stalwarts of the Society (though they occasionally had their papers
on music theory topics presented for discussion), but rather focused their attention
and writing on musical topics as ends in themselves; and there was much to contend
with, during the century when most modem music theory was developed, within the
roiling context of what to do about tuning. While the major natural philosophers
addressed music in a multi-faceted, global sense for a variety of aims, musical
theorists were, by contrast, singularly focused on music in a strictly theoretical sense
in which it was central to the story of natural philosophy in the seventeenth century.
Where the Royal Society elites articulated a broad range of interest in scientific topics
related to the new philosophy and occasionally includied music because of its
connection to other kinds of knowledge, the musical theorists pursued defined aims of
developing music theory as they grappled with the tuning problem for polyphonic and
instrumental music. The groups overlap, of course; but this second were most known
as musicians and musical theorists, rather than natural philosophers who occasionally
43

wrote about music. The musical structures developed by these theorists is nothing less
than ideology... encoded in symbolic systems105 and so worthy of investigation.
Though scholasticism was still being taught in the universities into the
seventeenth century, neo-Platonism dominated Renaissance thought and launched the
seventeenth century, implicit in all institutions. If new-Platonism was concerned with
the realization of perfect forms,106 then the purpose of art was to demonstrate the
perfection in nature. As the foundation of beliefs about nature began shifting, art
became one site of contention about the Platonic ideals, questioning a moral,
meaningful, organic cosmos and the authority of the heavens in human affairs.
Musical writers advocated a variety of solutions to musical theoretical problems,
reflecting and revealing the shifting bases of philosophical beliefs through their
writing about music.
Questioning the neo-Platonic notion of the harmony of the spheres as a
metaphor for the heavens as source of order and authority for humanity coincided
with the changing notions of nature. As beliefs about nature dictate beliefs about
music, so music was central to the questioning of old assumptions, though in mostly
oblique ways. Musical writers did not set out to debate deep philosophical questions
of meaning and authority; but their contentious writing was an active site for that
debate, albeit unwittingly, and all the more so because the problem with Platonic
intervals, the tuning problem, was of necessity so central to their discussion.
105 Sharpe, Remapping, 94.
106 Sharpe, Remapping, 448.
44

Harmony of the spheresrife with correspondences in reflected realities of
heaven and earth; an ordered and interconnected universe of hierarchy and beauty; an
opaque, sacralized cosmos saturated with meaning and significancewas
metaphysically dependent on neo-Platonic ideas. This universe was in sharp
contrast to that which underlay the new philosophy. The latter demanded
taxonomical structure in the universe, its meaning transparent to human
investigation and experiment. Neo-Platonism was at cross-purposes to the new
philosophy and lost its central role; it was not so much attacked as dismissed. With
one foot still in the Renaissance, Bacon, at the beginning of the century, had tried to
reconcile the new philosophy with neo-Platonism; and Newton, at the end of the
century, was still pre-occupied with Platonic-based pursuits. But by the end of the
seventeenth century, neo-Platonism simply lost intellectual cache, out of joint with
the times. The [late] seventeenth-century neo-Platonic revival was... a doomed
attempt to reinvest an already fatally secular cosmos with the sense of sacred
home.* 108 109 The description of the cosmos envisioned by neo-Platonism was no longer
seen as useful.
The Platonic ideal in music dictated that the perfect intervals were to be
combined into compositions according to strict parameters based on consonances
emanating from God and nature, to be discovered by man. The ancient foundation of
music was number, as discovered by Pythagoras. Making good music meant choosing
Geneva, Astrology, 269.
108 Geneva, Astrology, 271.
109 Geneva, Astrology, 282.
45

the right numbers, the correct intervals to create perfect consonances.110 The
Pythagoreans conceived of this precise, number-ordered universe against the
materialistic universe of Aristotelian natural philosophy. Aristotle himself wrote of
the Pythagoreans that they believed mathematical principles, including musical ratios,
to be the constituent elements of the whole of nature, the ultimate reality. Boethius
(480-526) re-iterated that Pythagoras discovered the mathematical foundation of
musical consonances in the perfect intervals. Mathematics is the foundation for
harmony, spatial and musical.111 112 113 Because this was such an all-encompassing world
view, it did not willingly depart the philosophical stage.
Neo-Platonisms loss of intellectual cache had a specific meaning and
consequence for musical theory: from musical sound as number to vibration.
Consonances were no longer based on simple numerical ratios but on vibration. The
most concordant simultaneous tones were the ones whose vibrations coincided most
frequently and regularly. Numbers were no longer the cause but only the
representation of what was happening musically. Vincenzo Galileis exposure of
the imperfections in Platonic intervals in the late sixteenth century was the leading
edge of this dispassionate view of music informed by a mundane, knowable nature.
Music in the modem world now is instrumental (both figuratively and literally),
efficient, and harmonically calculated. Equal temperament tuning is the ultimate
110 Gozza, Number to Sound, 1.
111 Gozza, Number to Sound, 2-4.
112 Jamie Kassler, Inner Music: Hooke and North on Internal Character (Madison, Teaneck: Fairleigh
Dickinson University Press, 1995), 53.
113 Chua, "Vincenzo," in Clark and Rehding, Music Theory, 20.
46

rationalization of music; tuning thus rationalized for the purpose of fretted
instruments playing in harmony has lost magic and divinity114 and implies a nature
also thus diminished. Pre-modem music is highly rational in a literal sensebased on
divine ratiosthe rational agent of enchantment.115 Disenchantment of music
means no less than the untuning of the cosmos, the collapse of cosmic order.
Modernity views the disenchantment of musical theory and the rationalization of
tuning as obvious and inevitable.
But it was not so for seventeenth-century musical theorists or performers. The
latter had been making novel tuning accommodations for instrumental and complex
vocal music since the late Renaissance without confronting the philosophical
contradiction with Pythagorean intervals. They simply did what they had to do to
perform the music. This often meant mean-tone tempering: diminishing a series of
consecutive fifth intervals by a bit; but it worked well for only a few keys. These
ersatz temperament solutions were not systematized and only more or less
satisfactory, usually limiting the keys that a performer could play in. Just
intonation, Zarlinos system of using more intervals than in the Pythagorean
philosophy, still had the inconvenient problem, because of using pure intervals, of
music ending on a different pitch than the initial one: the basic problem of non-
tempered tuningthe octave is not preserved. Dutch philosopher Huygens contended
that good singers (unaccompanied) will compensate for this instability by holding the
original pitch in their headsin effect, creating their own tempered intervals. The
114 Max Weber, The Rational and Social Foundations of Music.
115 Chua, "Vincenzo Galilei," in Clark and Rehding, Music Theory, 22.
47

trick, apparently, according to Huygens, was to get them to sing a piece quickly
enough so as not to forget the original pitch.116
Seventeenth-century theorists, in engaging more directly with the
philosophical issues of music theory, typically accepted the necessity of some kind of
temperament adjustment while still holding on to ideals of Pythagorean perfection.
The logical and the ideal, then, co-existed through the century, the latter giving way
to the former only as neo-Platonism and the idea of cosmological harmony lost
intellectual space and became irrelevant, space then taken up by the new experimental
philosophy. The co-existence of the pragmatic and the ideal was not always peaceful.
Assumptions about nature informed musical treatises, which then became sites for
contested notions of nature and the cosmos, though the authors would not have
perceived them as such.
Probably the most noted and prolific treatise writer of the early century,
Thomas Morleys most important treatise on music theory was an instruction manual
for singers and plucked instrument players on the intricacies of improvising two,
three, four, five, six, or more parts on a plainsong melody. It is far from being an
exact science. Modem music theory developed, haltingly and piecemeal, as a
response to the increasing complexity of music beginning in the late Renaissance.
116 Walker, Studies, 112.
48

Morley consults various sources for a solution and a clearing of my doubt for his
117
own treatise and notes the diursity betwixt them
Morley is not shy about proclaiming his own theory. He directs the reader to
dispose your musicke according to the nature of the words... .if you have a graue
matter, applie a graue kinde of musicke to it... .when you would expresse any word
signifying hardnesse.. .make the harmonie like vnto it, that is, somewhat harsh and
hard but yet so it offend not... .sharpe thirds, sharpe sixes and such like. Going out
of tune is unnatural because these are given by nature, not human artifice.
Morley claims ancient sources for his musical writing, namely Plato for whom
music was a heauenly thing and profitable for the seeking out of that which is good
and honest... .and cannot be intreated or taught without the knowledge of all other
sciences.117 118 119 120 Morley also cites Boethius (fifth-century Roman philosopher and
mathematician whose five-volume De Musica informed music scholarship into the
seventeenth century), who did notwithstanding write more of musick than of al the
other mathematical sciences and if it had not beene for him the knowledge of
musicke had not yet come into our Westeme part of the world. Morley cites these
ancient sources to lend credibility to his own writing; but, despite his stridency about
other musicians, he does not break any new ground about the philosophy of music,
117 Thomas Morley, A plain and easie introduction to practicalI musicke set downe in forme of a
dialogue....with many profitable rules to that effect (London: Peter Short, 1597), "To the Curteous
Reader," page unnumbered.
118 Morley, A plain and easie, part III, 177.
119 Morley, A plain and easie, part III, 183-184.
120 Morley, A plain and easie, part III, 184.
49

content to simply cite ancient sources without challenge even while suggesting
pragmatic temperament practices.
Everyone seems to have his (virtually never her) own composition and
performance rules, and Morley claims to organize the chaos. He anticipates that many
will read his book merely to find something for which to attack him by saying he is
undercutting other practitioners with his own methods for making music; he
proactively counter-attacks. [T]his booke will be so farre from the hinderance of
anie, that by the contrarie, it will cause those whome they alledge to be thereby
damnified, to be more able to giue reason for that which they do. possibly an
allusion to temperament practices, although he does not specify that. Anyone who
thinks to have all the answers and condemns others is a fool, imagining that all the
guiftes of God should die in themselves, if they shoulde bee taken out of the
worlde.121 122
The tension is almost palpable, even from the distance of 400 years; and the
intensity of feeling seems a symptom of the challenging of closely held beliefs that
underlay developing musical theory. Over the course of the century, the iron grip of
these previously unquestioned beliefs about the nature of the cosmos as they impacted
the practice of music loosened, not because anyone proclaimed it should be so but
because a dogmatic adherence to Pythagorean perfectionism became inconvenient, an
intellectual hanger-on. But early in the century, the intensity of feeling expressed in
Morleys treatise suggests a deep unease about the changing foundations of authority.
121 Morley, 'To the Courteous Reader," in A plain and easie, page unnumbered.
122 Morley, A plain and easie, Part II, 115.
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Thomas Ravenscroft, in 1614, took on changes in practice and philosophy
more directly. Music is being mightily abused in this braine-sick Age wherein we
liue,... neither Her selfe, nor her Lawes are regarded euen of her Children but
most.. .runne after their owne rebellious Imaginations; musicians pursue their own
priuate ends... pretending to Musicall Genius, and a religious disposition. These
Golden Sheepe, who are better Clad then Taught,... are willing to prostitute
themselues to Dance after euery mans Pipe. He equates the discordant state of
music with a commonweal which he sees in disarray. Let Common Practice and her
Complices censure me as they please,.. .1 ayme.. .to vindicate Her from these
Salaecismes, and Barbarismes. He sees an ally in Morley, who did shine in the
Firmament of our Art, and did first giue light to our vnderstanding with his
Praecepts and who saw errors in the Common Practice but was loath to break
with ita pity, since, if he did, others would surely follow because of his
124
influence.
The upstart musicians of the Common Practice must be those who are
taking on sacred nature, defying Pythagorass divinely mandated precepts of music.
But I (says Ravenscroft) have searcht the very Originall of our Art, and
Etimologis...compard the Practise with the Theory, Nature with our Art...and I find
it.. .extracted from the Quintessence of Arithmetick in the Rules and Praecepts..
Those of the Common Practice depart from the Fundamentall Reasons of the 123 124
123 Thomas Ravenscroft, A briefe discourse of the true (but neglected) use ofcharact'ring the degrees
(London: Edward Alide, 1614), opening Apologie.
124 Ravenscroft, discourse, Apologie.
51

125
Grounds and Rules of our Art. Following the first section of the Apologie, a series
of noted musicians of the day vehemently proclaim the rightness of Ravenscrofts
stance. Ravenscroft then concludes the Apologie by saying that concord and discord
exist in all the arts, not just music; and he views himself as a messenger of peace to
the chaotic state of music, to bring it back into concord and harmony with nature.
Both Ravenscroft and Morley, then, are almost pleading for a return to basics,
to the ancients wisdom about a cosmos based on perfect mathematical intervals and
harmony, even though they had to use some kind of tempering to perform music.
With their traditional stance, they are eschewing Bacons roughly contemporaneous
call to end speculation in music and just investigate it, as any other facet of nature;
but there is no evidence that they either one knew or cared about Bacons
experimental advocacy.
The first major theorist to accord with Bacon and to approach music
experimentally rather than mystically was William Brouncker, future Royal Society
president and translator, in 1653, of Descartes 1618 Compendium musicae.* 126The
introduction to the translation also included Brounckers own idea for dividing the
scale with logarithms, the very anti-Pythagorean notion of dividing intervals into
equal partsthe first one to propose this kind of manipulation. He wished to contest
Descartes claim that the consonances are based on arithmetic and show that their true
Ravenscroft, discourse, Apologie.
126 Still, Descartes relates in the Compendium that when drum skins of a wolf and a sheep are struck
simultaneously, the sheepskin will remain silent for fear of the wolf.
52

127
relationship is geometric. Interestingly, though, he did not seem at all interested in
solving the tuning problem; in fact, his calculations for various ways of dividing
intervals do not preserve the octave, the whole point of tempered tuning. Also in
the introduction to the translation, Brouncker notes that the complete musician must
have competence in the entire range of subjects touching on music, including
mathematics and magicand experimental science, especially acoustics: a
Renaissance man and beyond!
Coincidentally, in the same year that Brouncker translated Descartes
Compendium musicae, Hugh Platt published The Jewel House of Art and Music and
Nature. It was an essay in the new philosophy on a mission to subdue, tame, and
correct nature, wildness, and exotica, a popular and pragmatic sourcebook of
human artifice to enhance nature. It was a distinct departure from Morley and
Ravenscroft and heralded increasing intellectual space for the practical over the
mystical. That space opened up even more at the end of the century as philosophers
focused on mathematical solutions to temperament tuning and investigated
consonances in the context of vibration science.
Even in the last quarter of the century, though, Thomas Salmon tenaciously
clung to the notion that the true consonances are those perfect ones given by
Pythagoras. He unrelentingly campaigned for musicians using just (untempered)
intonation to duplicate the ethical effects of music that the ancients experienced. His 127 128 129 130
127 Gouk, Music, Science, 142.
128 Walker, Studies, 117.
129 Gozza, Number to Sound, 20-21.
130 Austern, '"Tis Nature's Voice," in Clark and Rehding, Music Theory, 40.
53

Essay to the Advancement ofMusick (1672) first argued his point passionately. In
1688 he published A Proposal to Perform Musick, in Perfect and Mathematical
Proportions, in which he famously proposed complex mechanical appendages to
instruments to compensate for the tuning discrepancy while maintaining just
intonation; the system required interchangeable fingerboards and different frets for
each string and was wildly impractical. He even gave up trying to explain the details
131
and said that a mechanic would just have to figure it all out.
In Chapter 1 of A Proposal, Salmon surveys the history of music. In ancient
times, music had great power and flourished, then died during the Darkness of the
medieval centuries. The present time is witness to a new glorious age of music with
the potential of surpassing the ancients because of the advent of polyphony and many
kinds of instruments. All are beholding to the Excellent Genius of our Modern
Musicians. Because of these advances, one might conclude, says Salmon, that
132
nothing can be improved upon the present practice of music.
But wait; there is something. The ancients made music with the Accurate
Observation of Proportions, which the Soul is from Heaven informd to Judge of, and
the Body in Union with it, must Submit to. All the world agrees that the more exact
the proportions, the more excellent the music; a singer or instrument out of tune will
ruin the best composition. So it is a great error of the present day that the beauty of
our music is rendred Ineffectual, by tolerating so many unproportionate 132
Walker, Studies, 115.
132 Salmon, A Proposal To Perform Musick, In Perfect and Mathematical Proportions (London: John
Lawrence, 1688), Chapter 1, 2.
54

133
imperfections. Since the octave must be stable, some kind of tempering is in
order. Salmon goes on to technically detail the tuning problem on a Viol, but then
insists that the Perfection of ancient intervals must be used in the present day
also.133 134 135
In Chapter 3, Salmon launches into the explanation of his solution for the
tuning problem. I have Calculated my Tables to find the exact tuning discrepancy,
and a Mechanical Workman then can fashion a Finger-board that the player
simply adjusts for each key; but of course, each fret must be tuned separately. But he
has tested it and found it to be very convenient! Salmon does not presume to tell the
fashioner of the fingerboards how to do his job, as that artisans expertise will suffice
to find the best mechanical solution, possibly even better than the one Salmon himself
135
has envisioned.
Salmon admits that in a few instances, his system cannot correct the out-of-
tuneness. But this does not proceed from the defect of this Proposal, Nature it self
will have it so. Then he seems to mitigate that statement a bit. Scholars are not to
alter Nature, but to discover her Constitutions, and to give opportunity for the best
management of all her Intrigues. Still, he seems somewhat irked at nature for the
imperfections in the supposedly perfect Pythagorean intervals but concludes by re-
iterating that the proof is in the playing; his system indeed works.136 Salmon straddles
two epistemes: the ancients as the only true basis for music-making and the
133 Salmon, Proposal, Chapter 1, 3-4.
134 Salmon, Proposal, Chapter 2,13.
135 Salmon, Proposal, Chapter 3,17-18.
136 Salmon, Proposal, Chapter 3, 23-28.
55

recognition of ancient imperfection with a modem method to correct it. Like his
contemporary Isaac Newton, Salmon identified with neo-Platonism; and Newton
owned a copy of Salmon s A Proposal To Perform Musick, In Perfect and
Mathematical Proportions.
Another major treatise writer at the end of the century, William Holder,
manages to cite the ancients, offer pragmatic solutions for tuning, and add a religious
devotional. He describes Sound in General in Chapter 1 and Of Sound
Harmonick in Chapter 2, where he defines intervals in slavish detail, using both the
monochord and pendulums to illustrate. In Chapter 3, Of Consonance and
Dissonance, consonances are determined by ratios of vibration pleasing to the ear, an
aesthetic and natural rather than Pythagorean definition. In explaining the way
vibrations work, Holder says that playing two notes that are separated by only a half-
tone simultaneously causes such a Battel in the Air between their disproportioned
139
Motions, sucha Clatter and Thumping, that it will be like the beating of a drum.
Chapter 5, Of Proportions, explains the complex system of logarithms to
divide the scale in equal parts so to keep in tune, always keeping the diapason
(octave) constant; the discrepancy between the perfect and tempered intervals,
according to Holder, is approximately 1/53 of a diapason, which closely approximates 137 138 139
137 William Holder, A Treatise of the Natural Grounds and Principles of Harmony (London: J.
Heptinstall, 1694).
138 The monochord was used in two ways: to explain perfect Pythagorean intervals and to explain
ways of dividing the scale (or other intervals) into equal parts, usually as a solution to the tuning
problem.
139 Holder, Treatise, Chapter 3, 34.
56

the actual irrational number.140 This logarithmic system for equal-temperament tuning
is what Holder calls the Natural Grounds of Harmony.141 142 He notes that Euclid had
a fair Hint... when he measured the Diapason by fix tones and found them to exceed
the Interval of Diapason. But the ancients did not pursue this Way of dividing the
Systems. Holder is firm in saying, possibly for intuitive reasons, that only the
approximations to the irrational numbers that precisely define the tuning discrepancy,
not those Irrational Contrivances[s] themselves, should be used in creating equal-
temperament tuning.143 In conclusion, he proposes some questions that bear further
investigation: why do human voices at the same pitch sound so differently from one
another? why do the sounds of the respective instruments differ so from each other?
why do some people not love music? (He suggests an answer to this one; there is a
Falseness in the auditory nerve that distorts the sound.)144 Holder seems
unquestioning about being in that epistemological space between neo-Platonism and
experimental philosophy, and includes a heartfelt dedication and thanksgiving to God.
Francis North, in 1677, wrote an extended and innovative essay on acoustics,
dedicated to A Friend (possibly Hooke), noted in records of the Royal Society, and
credited with being the beginning of modern music philosophy by at least one music
historian.145 By this time, acoustics and experimental investigation of sound were
Holder, Treatise, Chapter 5, 67-84.
141 Holder, Treatise, Chapter 6, 97.
142 Holder, Treatise, Chapter 6,116.
143 Holder, Treatise, Chapter 9,142.
144 Holder, Treatise, Chapter 9,152-153.
145 Kassler, Jamie C., The Beginnings of the Modern Philosophy of Music in England: Francis North's 'A
Philosophical Essay ofMusick' (1677) with comments of Isaac Newton, Roger North and in the
Philosophical Transactions (Hampshire, England and Burlington, Vermont: Ashgate, 2004).
57

coming to dominate music discussion, with a continuing pre-occupation with the
criteria for concordant and discordant sound. Physical explanations were based on the
coincidence theory of vibration. North accepted this, but ranks consonances in a
different order than Hobbes and Galileo, for example, whose ranking was based on a
Pythagorean arithmetical scheme; he ignores proportions in favor of sensory
perception of synchronous pulses.146 * North was the first to investigate sound initiation
and perception as well as the way the ear works as intermediary between these two
processes, a novel empirical approach. He suggests adding quarter tones to some
notes as a way to preserve the octave and was the first to choose, from among the
148
twelve Greek modes, the two scales (major and minor) now in use.
Still, an aura of moral judgment in discussions of tonality and concord lingers
in Norths essay: concordant sound is good, discordant sound is bada vestige of
musics central place in the moral framework of the cosmos. Only pleasing harmony
is acceptable as a desired musical sound; discord is allowable only on the way to a
pleasing concord, when the ear is assured that it will be speedily resolved.149 Music
may also help the listener gain ethical insights because of its unique capability to
express human affect.150
Kassler, Modem Philosophy, 52.
Kassler, Modern Philosophy, 77.
Kassler, Modem Philosophy, 79-81.
Kassler, Modem Philosophy, 83.
Kassler, Modem Philosophy, 87.
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CHAPTER 5. THE NEW PHILOSOPHY: MUSIC AS SOURCE OF ORDER
The waning of neo-Platonism, as well as Aristotelian natural philosophy, was
in no way an indication of an increasing freedom from fear of disorder. Order anxiety
was pervasive across classes and order widely perceived as fragile, a mere veneer
sublimating anarchy.151 152 153 From the first decades after 1500, all of Europe experienced a
crisis of authority across all institutions and areas of human endeavor, including the
arts, brought on by the Reformation and a range of other social and political
changes. Thomas Hobbes conviction that only the state prevented the war of each
against each and that the problem of knowledge was the problem of order, led him to
reject the experimental philosophy. Knowledge must not be tentative or contingent:
absolute knowledge equaled social order. So for Hobbes, science must be premised
on secure first causes, not in the business of investigating or debating them; and the
failure of the new philosophy to proceed on a foundation of certain knowledge was no
153
less than an invitation to civil war.
Hobbes notwithstanding, the Civil War itself was not about abandoning order
but rather overthrowing monarchial anarchy; and afterwards, society seemed
collectively appalled at what had been wroughtregicide!and willing to become
acquiescing moderates at the Restoration. As old certainties about cosmological order
and authority became increasingly tenuous in the wake of the centurys religious and
151 Kevin Sharpe and Peter Lake, eds., Culture and Politics in Early Stuart England (Palo Alto: Stanford
University Press, 1993), 11.
152 H. Floris Cohen, The Scientific Revolution: A Historiographical Inguiry (Chicago: University of
Chicago Press, 1994), 210.
153 Cohen, Scientific Revolution, 213-214.
59

political upheaval, an epistemological vacuum opened up; and the new philosophy,
all about ruling and taming nature, filled that vacuum as a hedge against
disorder.154 The order offered by the New Science was correcting, subduing, and
classifying nature with human artifice.
It was the right role at a critical time for the new philosophy. The centurys
chaos interfere[d] drastically with the sense of mastery that knowledge confers.155
The sense of order was fundamentally shaken. This provided one impetus to put order
into nature by rationaliz[ing] strangeness and correcting] error.156 157 Early in the
century, Bacon had insisted that all errors in beliefs about nature should be banished.
Thomas Browne answered the call to eliminate what he called vulgar errors in his
Pseudodoxia Epidemica, in five re-issues, no less. Its organization is a metaphor for a
newly ordered world he was trying to help create. It was a profound shift to this
new source of order, one inevitably marked by ambivalence and befuddlement. Even
as Browne repeatedly heaps scorn on both fundamentalist religious ideology and
magical thinking, he unselfconsciously subscribes to the class prejudices of the time
in condemning the lower classes for being unenlightened in the new philosophy; and
his false dichotomy of the enlightened upper-class scientist versus the lower-class
ignoramus fails to appreciate the fact of elites practicing alchemy, oblivious to its
contradiction with the new philosophy, and laborers and artisans well-versed in
154 Austern, '"Tis Nature's Voice," in Clark and Rehding, Music Theory, 40.
155 Campbell, Wonder, 4.
156 Campbell, Wonder, 6.
157 Campbell, Wonder, 86.
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158
understanding and absorbing the new ways of thinking about nature. Browne is just
one who is reacting to loss of the old order by embracing the offer of a new one
dogmatically, in his case.
Rising from the ashes of the Civil War at a time, not coincidentally, when
England seemed anxious to leave all that disorder far behind, the conservative elites
of the Royal Society appropriated the role of director of the new structure of order. At
a time of unrest, sources of meaning and authority were eagerly grasped.158 159 Science
was promoted by the elites as a means of social control since it is everywhere the
same, not volatile and complex like politics. One argument for the new philosophy
was its social utility in maintaining order, a position articulated in Thomas Sprats
1667 History of the Royal Society.160 This is not an argument for social reform but
rather for benefiting elites in promoting the political and social status quo and
stabilityscience for elites, not the wider population. Where Bacon had forcefully
articulated science for social utilityfor the material benefit of allthe elites
repurposed the scientific endeavor, taking ownership of it as a force for social order
and control.161 Identifying the New Science with social order, rather than subversive
of it, propelled its acceptance; and for this reason, the break in order represented by
the Civil War was the single most important event for the integration of the New
Science.162 Moderate reformers morphed into social conservatives, the foundation for
158 Campbell, Wonder, 97.
159Jardine, Ingenious Pursuits, 39.
160 Margaret Jacob, The Cultural Meaning of the Scientific Revolution (New York: Alfred A. Knopf,
1988), 29-30.
161 Jacob, Cultural Meaning, 38.
162 Jacob, Cultural Meaning, 73.
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the Royal Society.163 Although the Societys strength waned toward the end of the
century, the science it had promoted became the foundation of a new epistemology.
The Societys method was to study nature through observation and
experimentation; it was vehemently non-partisan, scorning and eschewing anything
not purely philosophical:164 an ideal value-free space for scholarly pursuits. A true
history of nature, by purifying authors accounts of .. .partisan zeal165 was the goal,
toward which results of observation and experiment could be marshaled. Philosophers
wishing to join the Royal Society should be laying aside all idle shadowy notions,
[that] they may make a thorough examination of NATURE.166
The ideal, if totally unrealistic, principle of an ordered, value-free neutrality in
the new philosophy was a powerful draw after the disastrous rivalries of the Civil
War. In service of that end, several New Science philosophers wanted a language
transparent to all, a new lingua franca of normative scientific discourse, stripped of all
the richness, redundancy, and overtones of quotidian speech, signifying only and
precisely the signified and reflecting a demystified nature.167 Wilkins developed the
Wilkins Universal Language, used by Hooke to announce his balance spring watch
mechanism.168 The universal language projects were dropped because of the
impossible complexities involved.169 Attempts to create a language somehow devoid
163 Jacob, Cultural Meaning, 77-78.
164 Dear, Revolutionizing the Sciences, 118.
165 Henry Oldenburg (first secretary of Royal Society) in The Correspondence of Henry Oldenburg, eds.
A. R. Hall and M. B. Hall (Madison and London: University of Wisconsin Press, 1966), letter 2445.
166 Oldenburg, Correspondence, Letter 2372.
167 Geneva, Astrology, 273.
168 Jardine, Ingenious Pursuits, 317.
169 Geneva, Astrology, 280-81.
62

of human content inevitably foundered on the same inherent impossibility as that of
value-free science; but the belief of its possibility is evidence of the striving for
defined order and authority in the wake of political rupture and philosophical
dislocation.
Acknowledging Diversity with Loss of Celestial Harmony
As basic and long-held political, religious, and philosophical assumptions
became fodder for re-examination, a necessary corollary was the necessity of
acknowledging diversity. Although this sea change had been going on since before
the dawn of the seventeenth century, the Civil War forced recognition of a new state
of affairs. England, at Restoration, did not return to pre-war reality; the model of
harmony and organic order could no longer be sustained. The religious and political
conflict had come into glaring focus and could not be managed with a hegemonic
ideal of unity and homogeneity.170 Tolerance for differing views, accommodation of
diversity was the radically new challenge of the seventeenth century as it emerged
into modernity.
The first manifestation of the breakdown of unity, the Protestant Reformation,
meant that sources of communal order shifted from public ritual and consensus to
individual godliness; protestant spirituality was experienced individually rather than
communally, symptomatic of the dismantling of the narrative of unity as a useful way
to describe society. The fragmentation of religious belief presaged and hastened
170 Keith Thomas, "Women and the Civil War Sects," in Crisis in Europe 1560-1660, ed. Trevor Aston,
(New York: Basic Books, Inc., 1963), 335.
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accommodation of political and philosophical fragmentation. In this way, the
Protestant Reformation acted as a midwife for the future, a future defined by
secularism of the modern state in Western society.
The abandonment of unity was centered in the tumult within natural
philosophy. Much more than merely the seventeenth-century term for science, natural
philosophy was a more comprehensive belief system about cosmological structure
and meaning, the character of matter and of cause, and the proper basis for natural
knowledgenot conformable to any single modern discipline. Competing claims of
Aristotelian-based Scholasticism, neo-Platonism, and the new mechanical philosophy
characterize the entire seventeenth century; and interpreting the changes as a simple
case of natural philosophy sinking into oblivion as science brilliantly ascends is a
profoundly misreading of the cultural significance of all of the voices in the
conversation of the seventeenth century. The competing sources of authority, the
fragmentation itself, are the story of budding modernity.
In music, the waning of the ideal of unity meant the abandonment of the
absolute: intervals are not quite perfect and consonance is not an absolute quality, but
one of degree. Rather than based on perfect Pythagorean intervals, consonance came
to be recognized as the coincidences of the termination of frequency cycles between
two strings. Frequency ratios are not placed into discrete categories of consonance or 172
Patrick Collinson, The Birthpangs of Protestant England: Religious and Cultural Change in the
Sixteenth and Seventeenth Centuries, (New York: St. Martin's Press, 1988), 59.
172 Anstey and Schuster, Science of Nature, 1-2.
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173
non-consonance, but rather are on a continuum of consonance. So the idea of
concord changed from mystical numbers as the foundation to coincidence of sound
vibration. The most concordant simultaneous tones are ones that coincide most
regularly and frequently; infrequent or random tones are discordant. Numbers are no
longer the cause, but merely the representation of sound. Concord and discord are not
contradictory qualities but part of a continuum. This abandonment of the absolute
quality of consonance is both manifestation of and metaphor for the changes wrought
in seventeenth-century natural philosophy.
Continuing Religiosity With Philosophical Changes
The single characteristic shared among virtually all writers, philosophers, and
theorists alike is a profound religiosity. From the religious foundation of Bacons
agenda for the new philosophy to better the lot of humankind to Newtons
preoccupation with ancient religious revelation, this century was marked by the
primacy of religion. Even as the seeds of fragmentation, diversity, and thus
secularism were sown by the Protestant Reformation, individual writers consistently
and clearly articulated their religious commitments. This remains true even as ideas
of nature and the cosmos, of order and authority, were being renegotiated, as seen in
the musical treatises. 174
Claude V. Palisca, "Scientific Empiricism in Musical Thought," in Seventeenth-Century Science and
the Arts, ed. Hedley Howell Rhys (Princeton, NJ: Princeton University Press, 1961), 109.
174 Kassler, Inner Music, 53.
65

Still, this renegotiation in areas touching on religion created a cloud of
suspicion of atheism over the new philosophy. The College of Physicians, feeling
their status quo threatened by the new philosophy, hired an agitator to attack scientists
of the Royal Society as being anti-religious and so undermining the social order and
the common understanding of God. Accusations of irreligiosity, albeit by a paid
rabble-rouser, could be taken seriously. The crux of the attack was that the
mechanical God of the new philosophers is not omnipotent and so can no longer work
175
miracles.
Suspicion about the new philosophy was not limited to the uninformed. After
the Restoration, when the conservative elite dominated and busily institutionalized
the new science, Leibniz scorned the new philosophers seemingly contradictory
claims for a clockmaker God Who created the cosmos and stepped away to let it run
according to physical laws on one hand, while yet being interested in the minutiae of
human existence on the other.175 176 177 Some historians since have also read the new
philosophers religious protestations as somehow disingenuous, cynically crafted to
appease a doubting public. This reading, though, belies a historicist understanding
of this very religious century; and part of the answer for the conundrum of
continuing, sincere religious belief among the new philosophers rests on two notions
of God uneasily co-existing through Church history and brought into relief in this
century of upheaval.
175 Francis Oakley, Omnipotence, Covenant, and Order (Ithaca: Cornell University Press, 1984).
176 His scorn was particularly directed at Newton and became intertwined with their bitter rivalry over
which of the two was the first inventor of the calculus.
177 Oakley, Omnipotence, 73.
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The two notions of God refer to the dual powers of God, absolute and
ordinary, vying for primacy through the Middle Ages, Renaissance, and into the
seventeenth century. Gods absolute powers are philosophically aligned with
Platonism, which inhered in early Christian theology, and are associated with the
Great Chain of Being; God is not constrained by anything and is able and free to even
suspend physical laws, as in the working of miracles. By contrast, Gods ordinary
powers are philosophically aligned with Aristotle and became the dominant notion of
God with the influx of his (Aristotles, not Gods) writings in the twelfth century.
Gods ordinary powers are those of the God Who created a lawful cosmos and
adheres to those laws; as such, He is knowable and transparent to rational
investigation. Scholasticism, which enshrined this latter notion of God, dominated
Church teaching well into the seventeenth century, notwithstanding an attack by
fourteenth-century nominalists who maintained that God is inscrutable and not
amenable to rationalist analysisphilosophical adumbration of the seventeenth-
179
century scientific revolution.
The elite, post-Restoration new philosophers of the seventeenth century, then,
tapped into both notions of God, the dual powers of God, in claiming both a Creator
God of a lawful cosmos as well as a personal, unconstrained God Who could
transcend these laws if he wished (which He has promised by covenant not to do).
This was their stance against charges of atheism, a more embracing, not limiting, 178 179
178 The famous condemnation of Aristotle by the Bishop of Paris in 1277 was an attack on the
Aristotelian idea that God could in any way be constrained, including by divinely created physical
laws. The Bishop lost that battle.
179 Oakley, Omnipotence, 81.
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notion of God. Understanding these religious subtleties undermines the theologically
uninformed interpretation of seventeenth-century protestations of religiosity as either
naivete or deliberate obfuscation. One cannot know the minds of individuals, of
course; but certainly the prevailing sentiment of the century was one of sincere
religiosity.180 181
The religiosity permeated all of society and was not limited to some narrow
philosophicalreligious agenda of the elites. Musical treatise writers credited
religious motivation and inspiration for their efforts or simply alluded to God in
incidental ways throughout their treatises. In his 1588 treatise on vocal and
instrumental music, John Case declares that music has God for a father and nature
for a mother. The character of these allusions subtly shifted, not surprisingly,
through the century. Early on, references to the Divine actually embraced God, the
cosmos, and heavenly harmony. Late in the century, religion became disengaged from
natural philosophy as the new, morally neutral experimental science moved into
philosophys intellectual space; and Godly references are deliberate rather than
incidental, forceful re-articulations of that which seems threatened because no longer
philosophically necessary.
Religion, though still vitally important to individuals, necessarily engaged
differently with an emerging philosophy that was not dependent on moral meaning in
180 Earlier in the century, before the conservative, moderate elites dominated the New Science and
institutionalized it with the establishment of the Royal Society, radical Protestant reformers and new
scientists had formed a pragmatic alliance, united primarily in their opposition to the Roman Church,
though for different reasons. Puritan theological rigidity caused the breakdown of this tenuous
alliance well before the Restoration.
181 John Case, quoted in Austern, '"Tis Nature's Voice," in Clark and Rheding, Music Theory, 30.
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the universe; and this is apparent in music treatises. In his 1694 musical treatise
scientifically analyzing the division of the scale, William Holder still proclaims the
divine in music. Following a detailed discussion of intervals and tuning, Holden goes
on to state that Gods wisdom and goodness order the Nature of Harmony and are
more than we can hope to fully understand, although the search for answers must go
on. Music is an essential part of worship and should be used for our great Creators
Praise, as He is the Founder and Donor of it. Toward the end of the century, St.
Cecelia morphed into the patron saint of music, not her original role, as she became
identified with natures female embodiment of music (Musica). As nature lost its
cosmological significance, it became increasingly identified with religion. This
natural theology was in ascendance, compatible with the new experimental
philosophy.
Thomas Mace and Nicholas Brady both wrote, during the last quarter of the
seventeenth century, about the importance of music in praising God. Each treatise has
an anxiously persuasive tone, as if needing to justify its stance. Mace, a cleric at
Cambridge University, created a widely used and respected instructional manual for
singing correctly and in tune in church, so as to glorify God. Interestingly, he
dedicates it especially to the Discenting Ministry, who might not be initially
friendly to the idea of music in church; Mace is on a mission to convince them 183 184
Holder,Treatise, 54-55.
183 Austern, '"Tis Nature's Voice," in Clark and Rheding, Music Theory, 59.
184 Thomas Mace, Mustek's Monument, or A Rembrancer of the best practical musick, both divine and
civil, that has ever been known to have been in the world (London: T. Ratcliffe and N. Thompson,
1676), frontispiece.
69

otherwise. The first part instructs congregations of parochial churches how to sing
psalms well, or do not bother to sing them at all, and suggests how cathedral music
185
may be much improved.
In rhyming verse, Mace insists that clerics must lead by example, learning
music well to set a high musical standard as a model for their congregations.
Example is The Thing:/ Thers but One Way, which is, Your Selves to Sing. It is
better to not sing at all than to sing badly. Admonishing your selves, (in Sweet
Acchord)/ In Singing Psalms, with Grace unto the Lord./ Sed sine Arte, That cannot
be done,/ Et sine Arte, Better let alone.* 186 Ancient King David, psalm singer and
harp player, is the shining example of musical leadership, out in the world rather than
cloistered with books, able even to fashion his own musical instruments. How can
He [cleric] be a Judge of Good, or 111,/ When (in That Thing) Defectives He of
Skill?
Mace acknowledges he is speaking boldly, but knows that advocating for
music in church is True Doctrine. Departing from rhyme now, Mace says he may
be taking a position against the General Swing of the Times, but cares not about
offending those who reject his advocacy of excellent church music, the Sleight and
Trivial, people. Music is divinely mysterious, as will be obvious to anyone who
earnestly studies it, capable of stirring great religious ecstasy. Mace goes on to vilify,
with much name-calling, those who criticize his argument from a stance of ignorance
Mace, Mustek's, frontispiece.
Mace, Mustek's, first part, page unnumbered.
Mace, Mustek's, first part, page unnumbered.
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of music. Let Things Alone, you do not Vnderstand. He considers it a pity that so
few understand the wonderful-powerful-efficacious Virtues music has upon the
Souls and Spirits of Men Divinely-bent.188 189
Music sung in tune is a simile of God, while Jarring Discords are.. .a simile
of the Devil. Music is to raise souls to God, enhancing the worship experience. Mace
feels impelled to provide instruction in good singing to parochial churches to
189
counteract the shocking state of musicianship among non-cathedral congregations.
Very interestingly, he claims that singing in tune unaccompanied is a virtual
impossibility, even for a singer with a discerning ear; instrumental accompaniment is
required to keep both a solo singer and an entire congregation in tune. So natures gift
of music must be enhanced by human artifice; and the organ is the best choice. Even
an indifferent singer would be hard-pressed to sing out of tune with an organ guiding
the musical way.190 And Mace offers proof, real proof, of the efficacy of tuneful
singing, a thing most eminently remarkable. During a 1644 siege by three armies at
York Cathedral, which was filled with people, the cannon shot was unable to
penetrate the walls and all inside were kept safe because of the congregations
angelic, tuneful psalm-singing.191
In his discussion of cathedral music, following the parochial music section,
Mace attacks more directly the dissenters who eschew music in church. He says that
England has attained the highest level of art in church music composition; and to
188 Mace, Mustek's, first part, page unnumbered.
189 Mace, Mustek's, Chap. II, page unnumbered.
190 Mace, Musteks, Chap. V, 9.
191 Mace, Musteks, Chap. V, 19-20.
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refuse to use this divine resource for worship is to profane it. He then offers a prayer
that God will bring into Concord and Perfect Unity All Dissenting, Jarring, and
Discording Christians, so that they may have a Right Discerning of the True Worship
and Service of Him. Only then, in imitation of heavenly choirs, will worship be
acceptable to God. But Mace has only begun his diatribe against music-eschewing
dissenters. Beginning with Kind Ignoramus, he proceeds with a most vicious-
sounding castigation of those who would deny in worship that which Angels Love,
and Devils Abhor.. .which clearly differentiate]s Heavn from Hell. Apparently,
the bitterness of the banning of church music during the interregnum is little abated at
this point. The dissension and disunity for which there is not yet a political language
are yet capable of being expressed in art.
The bulk of the treatise, nearly 250 pages, instructs singers and
instrumentalists in the fine art of making tuneful music for the purpose of right
worship. Mace concludes with a general discussion about concord and discord that
almost reads as if written in the first part of the century because it emphasizes the
mystical character of music, something far more than the sum of the musical parts. He
reverts to the old standby of the stretched string to begin an explanation of intervals,
but, curiously, confines himself to explanation of the octave, repeatedly created by
halving a strings sounding length any number of times. (Perhaps Mace thought that
any complicated discussion of the tuning problem would distract from his core
message.) Music is characterized by Contra-Qualitieslove and hate, light and 192 193
192 Mace, Mustek's, Ch. V, 29.
193 Mace, Mustek's, "An EPISTLE To all Ignorant Despisers OF THIS Divine Part of MUSICK," 30.
72

dark, good and evilPerceived by the Conchords, and Dischords: Agreements, and
Disagreements, betwixt the 7 Distinct Tones.194 Music carries moral weight. But
Mace also demonstrates a more modem approach in moving beyond intervals to focus
on chords as well, especially the 1-3-5 chord, particularly harmonic because
reflecting the Holy Trinity. The concordance of three voices singing the tones
simultaneously is much more pleasing than hearing them sounded separately, the
reason for which is an occult mystery.195
Mace concludes by re-iterating than anyone who tries out his system of
learning to make good music will, in the process, discover musics mystical and
divine wonders and shall never after Degenerate into That Gross Sub-Beastical Sin
of Atheism.196 * He cannot resist a short adjunct section about the mystical power of
music, there being Nothing of Art, and Science, under Heaven, more Properly
Significantly, and Powerfully fit for Divine, and Contemplative Good Christians, than
It. Because of its spiritual and emotional power, music should not be used to stir
up, and Excite Lightness, Vainness, Jocundity, and Folly, but used only to serve
God. It is That Eternal, and Coelestial Language. Music retains mystical power;
but it is located squarely within the divine religious experience, with no connection to
neo-Platonic mysticism or Pythagorean perfect intervals. Even in his discussion of the
stretched string to explain the wonder of the octave, Mace avoids any mention of
Mace, Mustek's, 265.
Mace, Musick's, 267.
Mace, Musick's, 268.
Mace, Musick's, 270.
Mace, Musick's, 272.
73

these ancient sources, focusing exclusively on the religious foundation of musics
spiritual power.
Even later in the century, Nicholas Bradycleric and librettist for Henry
Purcellpreached a notable sermon evoking some of Maces themes.199 Brady
begins by cataloging events in the Bible celebrated by heavenly music, seeming to
belabor the point as he cites Bible verses focusing on the centrality of music on
numerous spiritually notable occasions.200 201 202 He concludes from this that music, both
vocal and instrumental, is used and approved of by God. [T]he proper Office of
Musick in the Service of God, is to praise him, and... we may observe in the last
place, how Signal an evidence God has been pleased to give of his avowd allowance
201
and approbation of music.
Religion, according to Brady, is the most entertaining thing in
Nature... encouraging the truest chearfulness, and not... condemning any Innocent
Delights. Those who would have religion consist of only Moroseness and
Austerity by banning music from worship have done religion a great disservice; and
it would be unnecessary to make that obvious point if it were not for a party of Men
who unaccountably find music in church extremely culpable. God Himself
enjoins man to make music; and the fact that the Heavenly Art is corrupted by
some is no reason to eschew it altogether. If that argument for its banning from
Nicholas Brady, Church-musick vindicated: a sermon preach'd at St. Bride's church, on Monday,
November 22,1697, being St. Caecilia's day, the anniversary feast of the Lovers of music (London:
Printed for Joseph Wilde, 1697).
200 Brady, Church-musick, 2-5.
201 Brady, Church-musick, 5-6.
202 Brady, Church-musick. 8.
74

religious use were reasonable, it would follow that poetry should also be banned from
religious use because of the debauchery of some verses. Music naturally directs us to
Mansions of Joy having in it something of Divinity.. .which acts upon the Soul
with such a sweet Violence. Alluding to recent political discord, a shattering of
the peace now mended, Brady offers a prayer that all the several parties in the
kingdom, however formerly divided by interest or design, would.. .resemble the
Trumpeters and Singers in the Text [Bible]... and [be] as one.. .in Praising and
Thanking the Lord!204 Brady concludes by saying he is sorry for those whose
unhappy Aversion to Divine Harmony, renders them unlike to the Saints and Blessed
205
Spirits who join with God in making heavenly music.
Like Mace, Brady makes mention of neither Plato nor Pythagoras in his
urgent advocacy of instrumental and vocal music in church. He speaks lovingly and
passionately about the mystical and divine properties of music, capable of moving
men to heights of joy and wonder, eliciting from them the best that God has put into
humanity. None of this has to do with ancient wisdom, though; it is all about the
Christian religious experience. The divinity of music is not to be found in number
mysticism but in its power to connect humans to the divine presence through this
divinely ordained art.
Brady, Church-musick, 10-12.
Brady, Church-musick, 17.
Brady, Church-musick, 23.
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CHAPTER 6. CONCLUSION
Music writing offers a window to illuminate the changes wrought over the
course of the tumultuous seventeenth century concerning sources of order and
authority. The fragmentation across political and religious institutions was mirrored
in profound changes in natural philosophy. As the narrative of the harmony of the
spheres lost intellectual space to New Science, treatises and other music writing
became sites for contested ideas about shifting intellectual spaces.
Religion seems to be a constant; writers throughout the century express deep
and sincere religious sentiments which are not apparently diminished by the new
natural philosophy or the fragmentation in religion itself. The constancy is an illusion,
though. Even if individual sentiment did not wane, the way in which religion engaged
with philosophy changed fundamentally. When the harmony of the spheres was
dominant, a unified vision of the cosmos with a place for everything (and everyone)
and everything in its place, religion was part of that unified scheme; it shared
cosmological space with natural philosophy. But as ideas of nature drastically
changed and the new experimental philosophy came into ascendance, there was no
longer any intellectual space for religion. Religion became extraneous: a personal
choice rather than a philosophical necessity. The urgent-sounding re-articulation of
the importance of church music after the Restoration attests to a growing, if still
unconscious, nervousness about the cultural role for religion when it no longer
mattered to the new philosophy.
76

When the cosmos was tuned to the music of the spheres, order inhered
throughout the universe, a given of human existence. But when the cosmic music was
silenced, order was no longer to be found in the cosmos. Humankind was now
unencumbered, free from cosmic control and the certainly that accompanied it. Order
must now be imposed by a newly autonomous humankind. Music treatises illuminate
that highly contested process, fraught as it was with such great cosmological
significance, revealing a deep level of discomfort as previously unquestioned
certainties are now fodder for debate. The level of vitriol is astounding as debates
were fought bitterly over issues ranging from the inconsequentialwhether or not to
label notes with syllable namesto the central problem of the Platonic foundation of
intervals. The bitterness and deep animosity among treatise writers seems to encode
the fear of the new reality of a desacralized cosmos.
The tuning problem, that the Platonic intervals were not perfect at all for
performing polyphonic and instrumental musicalong with the corollary issues of
the nature of consonance and the proper division of the scalewas the most critical
issue for the music world in the seventeenth century and was met by a variety of
responses that shed light on the way epistemological change occurred over the course
of the seventeenth century.
The tuning problem could not reasonably be ignored; musical performance
demanded some kind of resolution. For some, it was the elephant in the room. They
worked around itlimiting the music they played or the range of music, limiting the
keys they used to perform music, making on-the-spot adjustments to instruments or
77

individual tuning of instruments for specific piecesbut not confronting,
metaphysically or technologically, the core issue of the imperfection of the Platonic
intervals.
Of the other perhaps more philosophically-inclined thinkers and writers on
music, some may have been excited about the new experimental philosophy and not
sorry to give up cosmological certainty for the prize of new knowledge of nature and
a tuning cure for the inconveniently inadequate Platonic intervals. Bacon, though
not offering comment about tuning specifically, forcefully eschewed musical
mysticism. Hooke seemed unabashed by the metaphysical consequences of tempered
tuning, eagerly joining in the search for the most useful solution. Newtons entire
sense of reality was founded on Platonic mysticism, but he also joined in the musical
discussion of new kinds of tuning, commenting on Francis Norths essay on
acoustics, consonance, and the scale.
Most of the both philosophically- and musically-inclined were more mixed in
their confrontations with the tuning issue. They developed or subscribed to new
tuning paradigms while convincing themselves that, somehow, Platonic certainty still
inhered in the cosmos. This was Thomas Salmon, who invented ludicrously unwieldy
mechanical contraptions to fit on instruments so that musicians could still use just
intonation. Others saw various methods of dividing the scale into equal pieces to
develop a system of tempered tuning not as abandoning but rather redefining cosmic
harmony. The range of responses is witness to the shifting and re-alignment of
intellectual space in the seventeenth century.
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Because of this metaphysical and intellectual jostling, neo-Platonism and the
harmony of the spheres, cosmological certainty and a unified narrative of religious,
political, and cultural reality all were eventually squeezed out of meaningful
existence. But it was not because anyone made it so; and it was not deliberate,
systematic, or linear. Certainly there was never a conference called to discuss the
tuning problem and come up with a workable solution or fashion a compromise. Even
the kind of profound epistemological change such as occurred in the seventeenth
century is piecemeal, unconscious, at times retrograde. There is no zero-sum game of
experimental philosophy or tempered tuning advancing and taking over the old
cosmological thinking. Music lost cosmological significance, not through willful
advocacy, but because it ceased to be an important way to view the cosmos.
No one in the seventeenth century, even the brightest and most prescient,
could have surveyed the sweep of the century and announced the epistemological
shift. There is no announcer, neither declarer nor decider. The paradox of historical
change is that it occurs only through sentient, willful actors; yet what is wrought is
unforeseen, little understood, and largely unintended, always prey to some level of
historical contingency, and written in the passive voice. People through the century
placed a host of meanings on the political, religious, and philosophical upheaval; and
change happened, fundamentally and permanently.
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IDEAS OF ORDER IN SE VENTEENTH CENTURY MUSIC WRITIN G Melanie K. Brooks Nelson B.A., University of Illinois, 1977 A thesis submitted to the University of Colorado Denver in partial fulfillment of the requirements for the degree of Master of Arts History 2012

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2012 by Melanie K. Brooks Nelson All rights reserved

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This thesis for the Master of Arts D egree by Melanie K. Brooks Nelson has been approved for the Master of Arts in History by Carl Pletsch, Chair Carl Pletsch Advisor Richard Smith Gabriel Finkelstein April 8, 2012

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Brooks Nelson Melanie K. ( M.A. History ) Ideas of Order in 17 th Century Music Writing Thesis directed by Professor Carl Pletsch ABSTRACT England in the seventeenth century was in the midst of turmoil: political, religious, and scientific. Civil war and regicide, puritan dissension, and a fundamental shift in the perception of nature all challenged the presumption of unity encoded in the no tion of the harmony of the spheres. The very foundation of order and authority was at stake; but because the presumption of unity had prevented the development of a language of diversity, the historian has few sources f or the transparent expression of conf lict to mine for cultural meaning. The arts though are rich, albeit less than transparent, sources for investigating conflict; and because the harmony of the spheres was more than mere metaphor but perceived to be the very structure of the cosmos, seventee nth century musical writing especially, both by well known natural philosophers and by lesser known musical theorists, encodes shifting notions of authority and order. These writers both created new musical theory and disputed theoretical issues, especiall y that of temperament tuning: the necessity to modify the heretofore perfect Pythagorean intervals to accommodate modern musical instruments and polyphony. In challenging the perfection of Pythagorean intervals and in claiming musical theory to be the prov enance of human creation rather than of nature, musical writers were prognosticators unaware, trumpeting the shift to modernity as humanity wrested control of its destiny from the cosmos. its publication. Carl Pletsch

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ACKNOWLEDGEMENT I wish to thank my advisor, Carl Pletsch for insights that guided me to core issues in my research.

1 CHAPTER 1. I NTRODUCTION In the late sixteenth century, the Rosicrucian scholar Robert Fludd diagrammed a Christianized concept of the Pythagorean monochord, the harmony of the world in pictorial detail, displaying the musical order imposed by God a speculat ive, all encompassing cosmological scheme Calling it the Divine Monoc hord, his detailed chart consists of two octaves, with internal intervals designating hierarchical elements of the universe: earth, God, highest heaven. and microcosm was 1 But his intricately constructed scheme amounted to the vain attempt of one and religion, which by then on the cusp of the seventeenth century, had been irrevocably sundered 2 s was 3 It was the Renaissance and it was modernity: divine right of kings and self governance; natur al magic and natural philosophy; harmony of the spheres and the silencing of the harmony; the great chain of being and the taxonomy of nature; Truth and facts; m organic nature and man nature; music of numbers and music of sound; Pythagorean perfect intervals and 1 Anthony Aveni, Behind the Crystal Ball: Magic, Science, and the Occult from Antiquity Through the New Age (New York: Times Books, 1996) 81. 2 Jamie James, The Music of the Spheres: Music, Science, and the Natural Order of the Universe (New York: Copernicus, 1993), 128. 3 Joscelyn Godwin, Music, Mysticism, and Magic : A Science Book (London, New York: Routledge and Kegan Paul, 1986), 143.

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2 tempered tuning. Whatever one call s the transformation during the long seventeenth century the Scientific Revolut ion writ large or small England at the end of the century was a world fundamentally changed from the England of the la ter sixteenth cent ury. T he transformation though, far from being linear or cumulative, was marked rather by shifting and shared intellectual spaces, conflict and conflation recession and ascendance, anomaly and concordance. The philosophical debates that so consumed thinkers and writers early on were left behind by the end of the period, not so much resolved as peripheralized. The century was witness to an epistemological shift none could have foreseen The intellectual upheaval was defined by changing and diversifying sou rces of authority in natural philosophy, politics, and religion. By the end of the century, the notion of a harmonious cosmos had lost both its intellectual bite and its cultural meaning as a shared perception of reality. The first Stuart king of England, James I (James VI of Scotland), ruling a fter Elizabeth f rom 1603 1625, continued her priority, formalized in the Elizabethan Settlement, of maintaining harmony and a vision of unity within society, the via media 4 treading a moderate path that rejected extr emism in religion and politics and elevated civil peace as the supreme good. The beginnings of a fundamental breakdown in this harmonious perception of reality were evident in religion and politics; and n atural philosophers were already experimenting and exploring beyond Renaissance fra mes of reference, rethinking assumptions about nature and the cosmos. But both Elizabeth and James, through sheer force of powerful personae a nd 4 Alister McGrath, In the Beginning: The Story of the King James Bible and How It Changed a Nation, and Language, and a Culture (New York, London, Toronto, Sydney, Auckland: Doubleday, 2001), 160

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3 ability to cajole, persuade appease, and manipulate were able to maintain the appearance o f unity and harmony even as its breakdown was increasingly manifest in natural philosophy, religion, and politics. The rule of Charles I beginning in 1625 wa s not marked by the political ability or force of personality o f Elizabeth and James; he lacked the gift s to contain the increasing fragmentation evident in society. His c onstant plying Parliament for more funds taking a Catholic bride, and choosing an archbishop widely perceived to be m uch too cozy with Rome all served to raise the alarm of the people about the maintenance of order Where James had been able to placate and sustain the status quo, Charles angered and, fatally, lost the trust of the people to rule for the common good and to maintain order. The fall of the monarchy, regicide, and the inte rregnum Commonwealth far from being assaults on order, were attempts to restore order within a society whose fear of chaos ranked almost equally with fear of eternal damnation. Far from a clarion call for democracy, t he condemnation of Ch arles and turn to Parliament rep r esented a desperate pursuit of an alternative source of unity and order as monarchial disorder ran amok. But unity, real or perceived, was never again to be. The mid century break of the Civil War and Commo nwealth was more than political, m ore even than religious. A changed society emerged from the grist of that mill shocked at what had been wrought in the beheading of a king, 5 but never again to wholly trust king or Parliament; agonizingly anxious to restore order and enforce civil conformity, but 5 McGrath, In the Beginning 289.

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4 forced to recognize fragmentation of authority in religion, politics, and natural philosophy. The Restoration of the monarchy was no t a return to former times, but a new tacit agreement between people and king that the latter must accommodate the former in new ways; Wi lliam and Mary sailing into London in the Glorious Revolution of 1688 made manifest the changed relationship betwe en th e people and the monarchy. That changed relationsh ip was symptomatic of a shift throughout society, not announced or articulated and certainly not appreciated for the profound social and cultural change it represented nuanced and subtle yet utterly transformational. Even as that shift permeated society, it entered into artistic products, representations of shared cultural meanings. Art as ideological statement, that is, addressing noti ons of order and authority, illuminates the changed ep istemology from one of a unitary, harmonious source of cosmological order expressed in the great chain of being and the universal monochord to the recognition of diverse sources of authority; from the notion of absolute Truth to acceptance of good enough s tandards of truth; from God as immanent in an organic, holistic nature to God the Creator existing outside His Creation, a nature to be experimented on and manipulated by man. Just as fundamental changes in natural philosophy were part of the fragmentatio n of order and authority in politics and religion, so changing ideas about the role of music in the cosmos and about basic assumptions in music theory were e mbedded in the changing notions about nature and natural philosophy. Music was identified with the harmony and order that structured all of society, an identification

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5 that broke down as the reality of that harmonious unity in soci ety broke apart and music bifurcated into science and art, no longer the metaphysical glue of the cosmos. yet crept in like a thief in the night, neither noticed n or noted, predicted nor understood, like the unheralded entr ance of the general epistemological shift of the century. No one willed what happened or directed its occurrence; but by the end of the century, natural philosophy had become merely science, and humanity bore the full weight of responsibility for the creat ion of order and meaning in a cosmos devoid of both. The central role of music in the shift to experimental science in the seventeenth century it has been scantily studied in this connection. 6 Historians of music concentrate on t he history of method and p erformance practice, largely irrespective of complex intellectual connections and currents of the century; and historians of science have consigned music to the art category and thus not within their purview. More broadly, music in relation to natural phil osophy has not been duly investigated 7 Historians have largely ignored the centrality of music in 8 an omission of the intellectual map of that century. 6 Penelope Gouk, Music, Science, and Natural Ma gic in Seventeenth Century England (New Haven and London: Yale University Press, 1999), 19. 7 Jamie Kassler, The Beginning of the Modern Philosophy of Music in England (Aldershot, Hampshire, England and Burlington, Vermont: Ashgate, 2004), 2; Linda Phyllis music, natural philosophy, and the hidden world in seventeenth Music Theory and Natural Order From the Renaissance to the Early Twentieth Century eds Suzanne Clark and Alexander Rehding (Cambridge: Cambridge University Press, 2001), 31. 8 Paolo Gozza, ed., Preface, Number to Sound : The Musical Way to the Scientific Revolution (Dordrecht, Boston, London: Kluwer Academic Publishers, 2000) xii.

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6 Music writing of the seventeenth century is an integral part of cultural history as a rich source of ideological statement in a matrix joining reality, representation, and perception. 9 Culture is implicit in constructing reality; cultural representations 10 that is, notions of order and the control of disorder. Musical writing is an important piece within the wide ra nge of cultural practices of the seventeenth century in address ing ideas of order; investigating it helps redress its virtual omissi on About 100 treatises were produced in England in the long seventeenth century (1580 1720), more than in any other place. 11 Investigating these and other musical writing is a sort of discourse analysis to reveal ideologic al meanings within cultural practices, a way to examine questions of authority through thes e cultural representations. These not only reflect prevailing ideas of order and authority, but also inform and shape attitudes and beliefs: cultural discourse as id eological legiti macy and context for political statement. helps to avoid the pitfalls of imposed meanings, categories, and dichotomies in favor through cultural products an additional way to read the tumultuous events of the seventeenth century. 12 9 Sharpe, Kevin, Remapping Early Modern Engla nd. Cambridge: Cambridge University Press, 2000, 15. 10 Clifford Geertz, quoted in Sharpe, Remapping 17. 11 Rebecca Herisonne, Music Theory in Seventeenth Century England Oxford: Oxford University Press, 12 Sharp e, Remapping 18 19.

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7 T aking this cultural turn in intellectual history by reading musical writing has resonance on an other level for the sevent eenth century. Musical writing as a cultural expression has to do with or der, not only in the general sense as in any historical c ontext; it also directly relate s to the commonweal of the seventeenth century because of a continuing and pervasive belief in correspon dences and analogies through most of the seventeenth century. These normatively depicted the cosmos as an interconnected hierarchy a representation, not a metaphor and writers of the time were clear about the distinction. Truth on one level of meaning translated to truth in another; this system of analogies was wide ly accepted and virtually unquestioned. 13 Music was identified with order through the harmony of the sphe res and the universal monochord. O rder was the very fabric of the universe, expressed and organized by music ; 14 and t he tortuous route of the lost intell ectual cache of this pervasive belief is a critical piece of seventeenth century intellectual history. As part of its being a cultural representation of ideas of order and authority, music occupies the same intellectual space as natural philosophy in the seventeenth century the former expressing identical notions of order and disorder, attitudes toward na ture and sources of authority as the latter. England was thrown into epistemolog ical ferment after papal authority was dethroned; writing about music is o ne way to view the ensuing intellectual debates political, religious, and 13 Sharpe, Remapping 44. 14 James, Music of the Spheres 3.

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8 philosophical. 15 The same network of practitioners of natural philosophy also wrote about music in a s pecula tive mo de; that is, although they occasionally addressed issues in musical theory, including the vexing one of tunin g they wrote more broadly about the underlying mathematical and physical principles of music beginning with that iconic advocate of the experimental philosophy, Francis B acon, an d including Hooke and Newton 16 Still, h istorians have be en slow to appreciate the importance of musical models Musical treatise writers in England, who seemed nearly obsessed with order in their construct ion of a complex edifice of musical theory, incorporated the new thinking about nature and order in their writing. Musical writing, like the New Science in the seventeenth century, acted as a k ind of code for imposing order; but the code creators themselve s were unaware of their role in the changing epistemology. To this end, then, musical theorists both participated in and perpetuated new ways of thinking of nature and music, even as they unselfconsciously continued alluding to earlier Pythagorean musical notions of order and authority. T hose wri ting about music debated the urgent problem of tuning division of the scale, consonances, and the proper nature of intervals as well as more trivial ones: whether or not to attach syllable names, in addition to letter names, to the notes of the scale; the optimal number of lines on a staff; which note to assign to the bottom line of the staff. The musical theory emerged in the context and as a reflection of epistemological change; 15 Ann Geneva, Astrology and the Seventeenth Century Mind : William Lilly and the Language of the Stars (Manchester, New York: Manchester University Press, 1995), 40. She uses as trology as a similar mapping device for the debates of that century. 16 Gouk, M usic, Science 3, 25.

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9 so musical texts were sites of p hilosophical debate, albeit unconscious and non transparent. The distinction between natural philosophers using music al models and musical theorists writing about music though, is a difference of intent Both addressed, in varying texts, changing ideas of music and music theory that were an integral part of the more general intellectual ferment in natural philosophy. I ntellectual sites then, for the new musical theory being threshed out were the same ones as for the new experimenta l philosophy, e mbedded i n changing notions of nature and of sources of authority; and all musical writing of the seventeenth century experimental to practical, constitutes a single body of musical discourse mapping the intellectual upheaval of the century. That the upheaval resulted in a foundational philosophical shift by the end of the century was entirely an unintended consequence.

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10 CHAPTER 2. CHANGING BELIEFS ABO UT NATURE AND MUSIC These writers address ed not only the tuning problem but a range of iss ues rela ting to music theory, creating most of the musical theory structure in place today. Beliefs about nature inform music, always; and ideas about the natural order, though having the gloss of immutability, are culturally determine d. Music writing throughout history attest s to both its role as agent of change and its susceptibility to be changed by culture. 17 As ideas about nature change, so do ideas about m usic. Nature imposes order on music theory, legitimizing it and providing authority for rules that, because seemingly based on nature, appear to transcend culture and history. 18 This illusion is than certai n knowledge 19 in the seventeenth century. Even thou gh t ruth was no longer certain, the metaphysical search for it just did not matter anymore; reasonable standards of truth about observable nature held sway. Importantly, though, as th e new natural philosophy narrowed into experimental science, abandoning any claim to absolute Truth, it still retained its claim to universality, thus establishing its hegemonic claim 20 Just so, music morphed from a cosmological, mysterious, metaphysical construct to a pursuit accessible and su sceptible to scientific inquiry. Music was 17 Gozza, Introduction, Number to Sound, 29. 18 Clark and Rehding, Introduction, Music Theory 2. 19 Karl Popper, quoted in Clark and Rehding, Music Theory fn 5, 2. 20 Clark and Rehding, Introduction, Music Theory 8.

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11 contained and tamed, just as nature was in the seventeenth century transparent, dissecti ble: 21 Music was linked with astronomy in the quadrivium and followed it from occult to disenchantment of the world, 22 a powerful metaphor for the cultural transformation wrought during the seventeenth century and played out in music. The harmony of the spheres was 23 Before the new science was legitimized, though, experiments were carried out with some secrecy because of its association with natural magic. Only after the Restoration and with the establishment of the Royal Society did experimental science sufficiently separate itself from natural magic to be in the open. London became its intellectual center, rather than the universities, because of t he Royal Society; and inhabiting the same intellectual spaces as experimental science music became paired w ith it leaving behind its cosmological association with the harmony of the spheres. 24 The Tuning Conundrum ove, with science, from the cosmological to the mundane universal meant that it was now fair game for a nalysis and theoretical reworking 21 Clark and Rehding, Introduction, Music Theory 6. 22 This term was apparently coined by Friedrich Schiller and famously appropriated by Max Weber and the Frankfurt School. In Clark and Rehding, In troduction, Music Theory 6. 23 Gouk, M usic, Science 17. 24 Gouk, M usic, Science 54 55.

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12 25 Scientists and theorists writing about music argued vehemently about a range of issues relating to music theory, none as central as the problem of tuning. If one begins at the tonic or root descends in fifths or fourths or any other pre determined interval, one will never a rri ve precisely at the octave. I ntervals of a fifth plus a fourth, for example, should add up to an octave by Pythagorean reckoning; but they actually overshoot it by a bit Similarly, the twelfth pe rfect fifth and the seven th octave from the starting point should culminate at t he same point; but they do not. That specific discrepancy, the tonal distance between the twelfth perfect fifth and the seventh octave is the definition of the Pythagorean comma, the core definition of the tuning problem. Pythagorean perfect intervals are not perfect, that is. When music making consiste d of a solo instrument or voice or a capp ella music, this acoustical gap was not even noted. But the advent of polyphonic music along with fr etted and keyboard instruments in the Renaissan ce 26 accurate tuning was critical for full y exploiting the diatonic system 27 Equal temperament tuning simply subtracts a few osc illations from the supposedly perfect intervals, a bit of fudgi ng not discernable to the average listener, to create twelve geometrically derived equal semitones (each equal to the twelfth root of two) that are, however, irrational numbers, very far in philosophical terms from the supposed perfection of the arithmetic Pythagorean intervals: tuning rationality in 25 Music Theory Clark and Rehding, 18. 26 James, Music of the Spheres 87. 27 Clark and Rehding Introduction, Music Theory 6.

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13 irrationality. T he se twelve tempered, irrational, half tone intervals within the octave now add up precisely to the octave interval a seemingly straightforward uncomplicated solution. But with what cosmological significance that solutio n is freighted; and this seemingly obvious resolution of the tuning problem became standard practice only at the dawn of the nineteenth century. Appreciating the seismic epistemol ogical shift that equal temperament tuning represents role through the Renaissance. The ancient foundation of music was number, from the Pythagoreans in the seventh to fifth centuries BCE. Making good music meant choosing the right numbers: that is, creating consonances with perfect intervals. These intervals were defined and illustrated by a monochord (invented by Pythagoras himself, according to tradition) a single stretched string with a moveable bridge. The octave, the most consonan t interval, is sounded by placing the bridge at precisely the middle of the monochord, creating a 1:2 ra tio of total string length to compressed length. The interval of a fifth, the next most perfect interval, is a ratio of 2:3, and the fourth, the next most perfect after the fifth, is created with a 3:4 ratio. The se intervals were t he most perfect, not prim arily for the sweetness of thei r sound, but because the

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14 integers used to form the ratios 1, 2, 3, and 4 were philosophically significant for the Pythagoreans. 28 Pythagoreans conceived a precise universe, ordered by number, against the materialistic univers e earth, air, water, fire that was the focus of Aristotelian natural philosophy. Aristotle, in the Metaphysics wrote of the Pythagoreans that they believed mathematical principles, including musical ratios, to be the foundation of everything, constituent elements of the whole of nature that were the ultimate reality. For them, nature is of mathematics and music. The noted medieval music theoretician Boethius (480 526) said that the Pythagoreans discovered the mathematical foundation of musical consonances. (Boethius himself surmised that there must be heavenly music because it was impossible to believe that the spheres could be moving silently through the heavens. 29 ) So the philosophical connection of music to nature and number has very ancient roots. 30 Music was identified with order, which was in turn identified with all of nature and philosophy ; order inhered in the universe, expressed and organized by music, and was the very fabric and organizing principle of the universe. The universe was seen as a totali ty, a unity; and all knowledge, morality, and purpose were included in that. Man filled a meaningful and knowable, if lowly, niche in the cosmological unity; his purpose for existence was intimately connected to the 28 The later medieval rationale for defining the fourth as dissonant was that, compared to the fifth, which was reinforced because of consisting of two thirds, the fourth had no such theoretical reinforcement. In Max Weber, The Rational and Social Foundations of Music Trans. and ed. Don Martindale, Johannes Riedel, and Gertrude Neuwirth (Carbondale: Southern Illinois University Press, 1958), 52. 29 Murray Schafer, The Tuning of the World (New York: Alfred A. Knopf, 1977), 260. 30 The format for this explanation is from Gozza, Number to Sound Introduction, 1 4.

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15 philosophical whole. The correspondence between earthly and heavenly music was as sumed, a manifestation of connected and communicating levels of reality All rightful place in the universe; the harmony of the cosmos a nd morality were inextricable. Harmony then, was more of a philosophical term than a musical one, applicable to any level of reality or of nature because of the complex system of correspondences and analogies that inhered in the universe. 31 The universe was perfectly tuned. To suggest, then, that the perfect Pythagorean intervals were not perfect after all was not merely to point out a mildly vexing issue requiring a technical fix as the problem might be framed today ; it was to assault fundamental assump tions about the universe the musical cosmos as the source of order, knowledge and authority, and to undermine the very foundation of Renaissance epistemology. The Renaissance view of the world, because it was so all encompassing, did not give way easily, qui ckly, or by a linear route And although the relentless onslaught of modernity in the seventeenth centu ry has the certainty of inevitability in hindsight, by no means would it have been viewed as such by the thinking about the cosmos only gradually lost intellectual cache as th e new scientific philosophy created ne w quest ions, priorities, and criteria to judge truth as it fill ed the space left by gradually outmoded Renaissance thinking. 31 James, Music of the Spheres 12.

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16 Four Early Philosophers on Music Robert Fludd and Johannes Kepler Vincenzo Galilei and Zarlino, w ere on the cusp of this change a round the change of the seventeenth century but could hardly have comprehended their pivotal place in intellectual history. part of a transition to. 32 For Fludd, t he monochord so central to Pythagorean music as number philosophy was more than a scientific instrument for defining and measuring intervals; as we have seen in his Christianized rendering of the Divine Monochord, tuning of the universe. 33 34 Squarely within the Renaissance tradition, Fludd was ho ld ing fast onto a world that was beginning to cea se to matter obsessed with the kind of symbolic thinking that was antithetical to the new philosophy. 35 Kep ler, his contemporary and also an ardent Pythagorean Platonist is by contrast, a n intriguing watershed figure, one foot squarely in the Renaissance and one in the new scientific epistemology; he heard the music of the spheres in full 36 Throughout his life, he immersed himself in a range of intellectual passions astronomy, astrology, theology, mathematics 32 Mary Campbell, Wonder and Science : Imagining Worlds in Early Modern Science (Ithaca and London: Cornell University Press, 1999), 29. 33 Gozza, Introduction, Number to Sound 4. 34 Godwin, Music, Myst icism, 105. 35 Keith Thomas, Man and the Natural World: Changing Attitudes in England 1500 1800 (Oxford, New York: Oxford University Press, 1983), 67. 36 James, Music of the Spheres 140.

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17 believing ardently in a fundamental connection among them and making it his life quest to discover it beginning with an assumption of the (polyphonic) harmony of the sphe res and scientific: amassing a wealth of data from his meticulous astronomical observations. Initially theorizing that the planetary orbits could be precisely inscribed within a defined series of geometric subsequently found that the astronomical data did not fit the theory. The scientist in him did not allow him to fudge the data, but the speculative Renaissance man refused to abandon his assumption of co smic harmony. An ardent Christian, he believed that G od must have created an alternative scheme that Kepler simply needed to work harder to discover. What eventually resulted, of course, were his laws of plan etary motion, still valid today, a grand synthesis of Renaissance and scientific epistemologies. Vinc enzo Galilei father of Gal ileo and a generation before Fludd and Kepler, was sufficiently independently minded and audacious to dare to expose the imperfections in t he Pythagorean intervals with simple experimental ev idence and to suggest a practical solution: tempered tuning. So he was the one to deliver the opening salvo of the assault on Pythagorean perfection. His pronouncement came in the context of a battle of words with fellow scholar and intellectual nemesis, Zarlino, who argued strenuously aga inst tempered tuning, insisting that singers instinctively use just (non tempered) intonation because it is from nature Vincenzo scorned this distinction, saying that no scale is intrinsically more natural than another Although

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18 he admit ted that he found the just (untempered) fifth to be sweeter than the tempered one 37 he personally knew many musicians who preferred the tempered fifth. 38 negated the idea of perfection in nature. Once t hat notion was dispensed with, the entire edifice of the harmony of the spheres was suspect. Zarlino, contemptuous of Vincenzo Galilei, still believed implicitly in heavenly harmony, perfection of nature, order, and the unity of the cosmos He vehemently rejected the skepticism of Vincenzo who contended that nature has no cognition, no intrinsic moral compass or exemplary models; the old ideas of consonances and supposedly perfect ratios were restrictive and incompatible with musical practice not natural at all but a product of human rationality. The aim of music, Vincenzo argued, was not to express perfection but to communicate. The debate between the two men was extremely heated, including vicious perso nal attack: not surprising given that, although ost ensibly debating the relative merits of just versus tempered intonation, they were in fact striving against one another about the nature of reality. leading edge of the dispassionate view of musical philosoph y and so of nature that was to dominate the modern world. 39 He did this in two ways: first, by objectifying music as a field for experimentation and second, by acting on this knowledge to 37 D. P Walker, Studies in Musical Science in the Late Renaissance (London: the Warburg Institute, University of London; Leiden: E. J. Brill, 1978), 19. 38 Walker, Studies 113. 39 Music Theory 17.

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19 propose a modern system of equal temperament tuning. 40 In pre modern music, both the cosmos and the soul are tuned to Pythagorean ratios, and earthly music is a reflection of the celestial spheres. The cosmos is connected to earth by a monochord reject that enchanted role of music in structuring and giving meaning to the cosmos 41 It is not an exaggeration, then, to say that 42 40 Music Theory 23. 41 Music Theory 22. 42 Gozza, Introduction, Number to Sound 39 41.

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20 CHAPTER 3. MUSIC AND THE NEW PH ILOSOPHY Through the ensuing century the new experi mental philosophy c ame into ascendance and music was central to the story, in two somewhat differen t senses. First, as noted music was identified with the structure of the universe in Renaissance thinking; so any challenge to the central role of music in cosmology of wa s t antamount to challenging epistemological beliefs Second, with the growing importance of polyphonic and instrumental music by the eve of the seventeenth century, the tuning problem had to be addressed Because of its importance in the intellectual convers ation of the time, experimental natural philosophers devised experiments and wrote about music, though usually not as an end in itself These included Francis Bacon, at the beginning of the century, Robert Hooke at mid century, and Isaac Newton writing Principia an d his later unpublished scholia The Royal Society, a gathering of gentlemen scholars chartered by Charles II in 1660 and pledged to taking up the gauntle t thrown down by Bacon to construct a new edifice of natural philosophy through experiment al investigation and observation participated in the musical conversation by offering a forum for discussion of musical experiments Aside from the well known experimental philosophers, less noted musical theorists wrote about music as a central concern, not as a way to elucidate other scientific ideas or to explore the nature of sound. These (mostly) men created an edifice of basic music theory that stands almost unchanged to this day, but also engaged in protracted debates with proffered solutions for a range of musical issues,

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21 including the tuning problem. These musical theorists were more narrowly focused than the new natural philosophers who had only incidental interests in music They did, nonetheless, respond think, and wr ite within the same epist emologically shifting milieu as the greater philosophers ; and their musical writing, as an art product, is also a source of i llumination about that tumult Each offer s hint s about the complex, non linear, even at times retrograde route by which the new ph 43 and the way mu sic figured in the grand conversatio n which was ultimately about sources of authority and order. Musical writing illuminates c hallenges to the Renaissance notions of the harmonic and moral structure of the cosmos and changing attitudes to ward nature : from an organic, unitary whole making up the Great Chain of Being with humanity having its place in that continuum, to humans as the objective observer s of nature, experimenti ng and investigating to reveal its secrets. Three Natural Philosophers on Music Bacon The name most firmly linked to the beginning of that is surely Francis Bacon early polemical tracts and the longer more fully developed works of his later years set the agenda for early experimental science and served as the methodological foundation of the Royal Society after the Restoration. In a century marked by the coexistence of still robust 43 Clark and Rehding, Introduction, Music Theory 8.

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22 Renaissance ideas a stands as a metaphor for the creation of new intellectual spaces. His experimental methodology is often cited as the hallmark of the revolution he helped lead; but his project transcended mere methodology to initiate a repositioning of man in relation to the cosmos and an alteration of the very foundation of ord er Had he foreseen the epistemological shift initiated by the new experimental philosophy as it was to meet the powerfully fragmentin g religious and political forces of the century, Bacon may have given serious pause to his strident advocacy of his philosophical agenda He unquestioningly embraced Renaissance thinking even as he advocated for the new philosophy. Natural magic, an experi ment based enterprise, flourished along with scientific investigation in that century, with no clear di stinction made initially. 44 Bacon himself was firmly planted in his own tim e, holding onto ideas ab out nature and natural phenomena that would later appear scientifically absurd ideas which his own proposed methodology would help dismantle. 45 He unabashedly betrays magical Renaissance thinking even as he writes about his new philosophy. In Sylva Sylvarum particularly, Bacon reveals the extent of his magical and alchemical thinking, incorporating unselfconsciously an astonishing array of magical beliefs into his explanations. 46 Though heralded as scientific innovator and 44 Charles Webster, From Paracelsus to Newton: Magic and the Making of Modern Science (Cambridge: Cambridge University Press, 1982), 2. 45 Richard Foster Jones, ed., Francis Bacon: Essays, Advancement of Learning, New Atlantis and Other Pieces (New York: The Odyssey Press, 1937) xxviii. 46 Paolo Rossi, Francis Bacon: From Magic to Science trans. Sacha Rabinovitch (Chicago: University of Chicago Press, 1968), 12.

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23 s of natural 47 Nevertheless, clear differences distinguish Renaissance natural magic and the new natural philosophy, consigning the one to historical obscurity and the other to philosophical dominance by the end of the century. The former focuse s on the unusual and the occult, promoting a sense of mystery, the latter on the ordinary and revealed book of nature, striving for transparency and the resolution of mystery. Still, ental methodology, the new philosophy (and Bacon, grudgingly) found common cause with natural magic, the two coexisting in a shifting intellectual space for most of the seventeenth century as natural magic gradually but inevitably lost intellectual cache e ven as the new philosophy gained intellectual ascendancy. While natural magic had its ascendancy in the Renaissance, Aristotelian philosophy dominated the pre Renaissance centuries; and Scholasticism continued to be taught in the universities through the first part of the seventeenth century. Bacon had only scorn for the failure of Aristotelian natural philosophy to actively investigate nature to discover cause and effect and for relying instead on pointless argumentation to no useful end. Aristotle is the 47 The New Atlantis New Atlantis: New Interdisciplinary Essays ed. Bro nwen Price (Manchester, New York: Manchester University Press, 2002), 84.

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24 48 Nature must be discovered through the (admittedly limited) senses, aided by experimental method. Ar istotelian rationalization is utterly fruitless 49 For the new experimental philosophy, Bacon envisions a marriage of nature and the rational 50 Scholasticism words w ithout actions, nature without investigation, talking without doing 51 -made Bacon hypothesis shy. He insisted that the aim of his new philosophy is the discovery of nature, not the construction of theoretical edifices. His idea of reform for natural philoso phy entails the construction of a complete natural history from the active investigation of nature before any theory dismissal of scholasticism and alchemy the other ever faileth to mu epitomizes his contempt. 52 The role of hypothesis in scientific investigation, now virtually unquestioned, was contentious in the seventeenth century because of its connection to Aristotelian speculative natural philosophy. 48 The Philosophy of Francis Bacon ed. Benjamin Farrington (Chicago: University of Chicago Press, 1964), 113, 115. 49 50 51 52 Bacon, Discourse in Praise of Knowledge in Farrington, 15.

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25 Scorn for Scholastic ism, that complex, rationalist enterprise to reconcile the teachings of the Church and Aristotle, prompted Bacon to insist on a rigid separation o f theology and philosophy. It was not a war between the two he fears, but rather an unhealthy entwining of the two, such as had dominated Western philosophy and theology for centuries. He saw this mingling of science and religion as pernicious. 53 Bacon continually emphasized the need to dis tinguish between Creator and Creation, between God and nature. Failure to do so was a fatal flaw of the ancients in their relationship with nature. Nature is evidence, but not the image, of God and must not be reverenced. It is indifferent to humans; so humans must impose art on natu re t o harness it for the good of humanity 54 Mixing the two conflates and confuses the divine with the natural and blurs the distinction between religion and science. 55 Early on, Baco n presided over a firm separation of the new natural philosophy from the religious enterprise, a bifurcation within natural philosophy, with all its unresolved tensions, that has persevere d to this day. Nonetheless, religion was the primary concern of most people in the sev enteenth century. So n ature joined Scripture as a new foundation of truth about God and the universe. Theories were reworked in the language of the New Science. These reworkings were normative in the way the old ones had been. New philoso phers believed that investigation into nature would ty and thus bolster faith. The reformulations advocated not 53 Rossi Francis Bacon 97. 54 New Atlantis 118. 55 Rossi, Francis Bacon 44.

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26 a break with religion, but adding nature as another field of divine revelation in this religious era. 56 This framing of new science helped legitimize it and armor it against accusations of atheism. Still, the storm clouds of vague associations with atheism hovered threateningly over the new philosophy; Bacon was prescient about the potentially awesome power of technology born of the manipulation of nature and believed that it must be tempered with and guided by knowledge of God, a moral restraint he would have assumed to be permanent and secure. 57 between atomism materialistic but with the taint of atheism and Stoical theory of pneuma uncomfortably close to reintroducing divinity into nature, philosophically untenable. But the cautionary religiosity Bacon saw as a permanent part of this re alignment was eroded and eventually destroyed by his own methodology; and so too notions of order became severed from morality and religion to become strictly human nature with the rejection of God immanent in nature set the agenda for the seventeenth century and is intimately linked to evolving concepts of order and authority. Bacon continually emphasizes the necessity of distinguishing between the Creator and His Cr 58 56 Natural Order: Historical Studies of Scientific Culture eds. Barry Barnes and Steven Shap in (Thousand Oaks: SAGE Publications, 1979), 98. 57 58 118. Also, early modern science was almost entirely a male pursuit. The fact that medieval institutions, most notably the hegemonic Church, were the exclusive realm of men meant that the institutions that grew out of that tradition continued to be dominated

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27 In music this meant a mov ement away from music as number to music as sound. Bacon stoutly rejects the notion of the harmony of the spheres and Platonic ratios as the foundation of the cosmos. Since physical, not mathematical, investigation of the universe is his aim, music is a se nsible acoustic event, not a source of mathematical speculations. This Platonic rejection, ironically, mimics Aristotle, who also rejected philosophical notions of cosmic harmony. Both Aristotle and Bacon, though, adhered to other Platonic ideas including a universe based on order and proportion and a belief in the moral and emotional power of music. 59 well as experimental philosophy. He thinks music can be used for utopian ends thr ough science and technology and is the first to propose a program for the empirical 60 The New Atlantis This work draws heavily 61 Though its setting is fantastical, Bacon insists this work is not a utopian vision but rather a realizable goal for a society properly employing technology for the good of humanity. 62 The paragraph on sound houses describes a magical technological approach to investigation: fetters of tra ditional Aristotelian philosophy; challenging gender roles too would likely have been beyond his ability to comprehend. In Revolutionizing the Sciences: European Knowledge and Its Ambitions, 1500 1700 Peter Dear (Princeton, NJ: Princeton University Press, 2001), 16. 59 60 61 62 James Spedding, Preface to The New Atlantis in The Works of Francis Bacon Vol. V, eds. James Spedding, Robert Leslie Ellis, and Douglas Denon Heath (New York: Houghton Mifflin, 1904), 351.

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28 We have also sound houses, where we practice and demonstrate all likewise great sounds extenuate and sharp; we make divers trembling sounds and letters, and the voices and notes of beasts and birds. We have certain helps which set to the ear do further the hearing greatly. We have also divers strange and artificial echos, r eflecting the voice pipes, in strange lines. 63 Bacon writes more generally about music as part of his plan for the new natural philosophy. In Sylva Sylvarum divided into ten centuries, each co ntaining 100 experiments, Century II focuses on music. The introductory paragraph is the most Music, in the practice, hath been well pursued, and in good variety; but in the theory, and especially in the yielding o f the causes of the practique, very weakly; being reduced into certain mystical subtilties, of no use and not much truth. We shall, therefore, after our manner, join the contemplative and active part together. 64 Bacon has little use for the elaborate stru cture of Renaissance music theory, based on Pythagorean intervals and mystical number relationships. As in all of his natural philosophy, he wants to investigate the causes of musical sound, in this case. He agrees with theorists that the octave is the mos t consonant interval 65 claiming ignorance in his Sylva Sylvarum of the octave unison relatio nship, for 63 Bacon, Works Vol. V, 407. 64 Francis Bacon, Sylva Sylvarum Works Vol. IV, 225. 65 Bacon, Sylva Sylvarum in Works Vol. IV, 226.

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29 example, since the foundation for Platonic intervals was well known, 66 is actually merely admitting he does not know about the connection between frequency of vibration and pitch, a discovery just making its appearance on the intellectual horizon 67 He goes on to suggest it must be that the air is forced into a regular pattern to give the sweet sound of the octave. 68 In the matter of the two half tones of the 69 So much for causes. Bacon agrees with Renaissance theorists in the order of the sweetness of interval consonances, except about the interval of the fourth. The question of the consonance of t his interval was much debated, but composers of polyphonic music needed it and were u sing it freely. Bacon favors the fourth as consonant, claiming some other yet, the fourth, which t 70 This is the pragmatic stance, admitting what was already virtually standard in musical practice. Study of consonances was of paramount concern to Bacon, as to every writer on music in the seventeenth century. In an intriguing di scussion about the causes of colours and order 66 Walker, Studies 120. 67 Gouk. Music, Science, 167. 68 Bacon, Sylva, in Works Vol. IV, 227. 69 Bacon, Sylva, in Works Vol. IV, 227 228. 70 Bacon, Sylva in Works Vol. IV, 228.

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30 Garden knots, good proportion, and symmetrical figures please; while irregular 71 Harmony equals beauty equals order. Order is loved, even revered, all the more so as the desperate hope of an early seventeenth cent ury society 72 an inquiry for another day app a rently, as Bacon does not investigate causes of har mony in Sylva Sylvarum He addresses the issue of musical sound though, describing experiments with various materials and instruments to produce a variety of pitches 73 but omitting, interestingly, any reference to the monochord. He is either ignorant of it or thinks, perhaps, the reference touches too closely on mystical Pythagorean number intervals. The intervening and concluding observations describe the creation and transmission o f sound and its connection with the percussion of air and vibration. A seemingly glaring omission is any discussion of the tuning problem, becoming acute because of the prevalence of both polyphonic music and fretted and keyboard instruments. Instead, Baco of Sylva Sylvarum focuses on finding causes for observed phenomena through experi mentation 71 Bacon, Sylva in Works Vol. IV, 229 230. 72 Bacon, Sylva in Works Vol. IV, 230. 73 Bacon Sylva in Works Vol. IV, 257 261.

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31 In disentangling Aristotelian philosophy from Christianity, Bacon unwittingly aided and abetted the sowing of the seeds of secularization by participating in the fragmentation of authority begun with the Protestant reformation. It is an outcome Bacon himself would have stridently condemned. Others through the century participated in the subor dination of mystical Platonic and Pythagorean philosophy in favor of scientific knowledge as the criterion for authority; virtually all of them too would have strenuously decried the materialistic, secularizing consequences of that action. And that is the ironic story of early modernity: the fragmentation of sources of authority and order, borne of an altered relationship to nature and sin cere religious sentiment. Hooke Later in the century, Robert Hooke was the consummate experimental investigator. As Rob Royal Society), he devised mechanisms for conducting course, the air pump, later to become a mainstay of Royal Society discussions and experimentation. H is enthusiasm for experimentation was recognized by the Royal Society, which named him the first Curator of Experiments and later Secretary of the In his experimental mode, Hooke relied on hypothesis testing, drawing sharp critic ism from Newton, who saw this methodology as anti empirical, muddying the waters by proposing imaginary, contrary explanations for natural phenomena already confirmed by experiment and

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32 observation. 74 Hooke in turn upbraided Newton for his dogmatism in stating with absolute certainty, for example, that he h ad proved his theory of optics and proposing his own alternate hypothesis for the data. 75 But far from being a dilettante, Hooke was an ingenious tinkerer, finding creative solutions to pr actical problems. 76 Even though he advocated a mathematical approach to the development of natural philosophy, his forte was inventing devices to further the cause of useful experimentation. 77 He helped advance the field of microscopy for his magnum opus, Mi crographia (1665 ) one of the few books published under the auspices of the Royal Society Also, Hooke found that he required a better light source than a simple candle or lamp to properly enhance the image from the microscope His answer the sotoscope, a liquid filled glass globe placed between light source and microscope and focused with a convex lens to direct the intensified light on to the specimen. 78 Hooke was not unaware of his creative gifts. On more than one occasion, he claimed to have found a clock based solution to that Holy Grail of seventee nth century science, the longitude problem. 79 While 74 The Science of Nature: Patterns of Change in Early Modern Natural Philosophy eds. Peter Anstey and John A. Schuster (The Netherla nds: Dordrecht, 2005), 229, 232. 75 Steven Shapin, The Scientific Revolution (Chicago: University of Chicago Press, 1998), 115 116. 76 Marcus Hellyer, The Scientific Revolution (Oxford: Blackwell Publishing, Ltd, 2003), 195. Hellyer maintains that twentieth century historians of the scientific revolution fail to appreciate the extent to which seventeenth century natural philosophers pursued science to solve practical problems. 77 Hellyer, Scientific Revolution 180 181. 78 Lisa Jardin, Ingenious Pursuits: Build ing the Scientific Revolution (New York: Random House, Inc., 1999), 44. 79 Jardin Ingenious 51. It was not until the latter part of the eighteenth century that John Harrison found a clock based solution to that vexing problem of navigation. In Longitude Dava Sobel (Middlesex, England: Penguin Books, Ltd., 1996).

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33 confidence that instruments such as the microscope and telescope would adequately compensate for these shortcomings. 80 Hooke thought about more than experiments, though. He believed that the ancients possessed great philosophical truth, but that it had become severely 81 Like m ost other natural philosophers of the time, Hooke professed a personal godliness and religiosity. Under his microscope lens, he saw revealed such perfect adaptation between structure and function that 82 Also coincident with most of his peers in natural philosophy, Hooke believed t he everlasting structure 83 Musical inves tigation constituted an important s experimental agenda, mostly relating to the nature of sound, ranging from vibrations and acoustics to the nature of harmonious intervals and the effects of music. He understood sound as vibration and, more importantly, related frequency to pitch in his experiments. 4. In addition to the experiments presented to the Royal Society Hooke presented papers focused more on the effects of music to a secret Philosophical Club, formed in 80 Shapin, Scientific Revolution 93. 81 Hooke, quoted in Shapin, Scientific Revolution 75. 82 Hooke, quoted in Shapin, Scientific Revolution 144. 83 Hooke, quoted in Shapin, Scientific Revolution 153.

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34 the mid 1670s by Hooke and others including Christopher Wren and William Holder, interested in musical topics In papers probably prepared for this g roup, Hooke hypothesized that nature has constructed the ear to receive sound exactly as it is produced, that is, in the same fr equency. The consonant intervals (octave, fifth, fourth, etc.) are pleasing and harmonious, not because of mystical Pythagorean numbers, but 84 & deli mathematical intricacies of the music to make it pleasurable. This is possible because God has created both the world and humans according to mathematical, geometric principles. 85 Hooke, along with Newton, saw music as the underlying structure of the universe, 86 an idea that seemed to peacefully co exist with his cutting edge experimentation on vibration theory. He constructed musical models, not primarily to explain musical princ iples, but to elucidate his natural philosophy in the context of connecting vector. 87 This notion is, of course, essentially Pythagorean; and Hooke unabashedly subscribed to this Renaissance idea to design experiments and create 84 Music Science 200 and 207 ideas, likely for the Philosophical Club. 85 Music, Science 212 213. 86 Gouk, Music Science 225. 87 Gouk, Music Science 213.

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35 explanations: music as a means to an end rather than an end in itself. Most notably, he compared the minute pa rticles constituting matter to the action of vibrating strings to explain the nature of matter and conducted experiments in acoustics and musical vibration to articulate and fortify his own theory of vibrating matter. 88 Again, he used musical analogies when detaili ng his theory of color by comparing the spectrum to musical harmonies and his notion of light by comparison to sound waves. 89 Hooke also weighed in on musical issues in their own right, including musical notation and division of the scale. His approach was, typically, a combination of Pythagorean mysticism and experimental practicality, his ideas on these matters based on widely hel d ideas of the time, not original but rather his own unique presentation. Whether to give names to the twelve tones of the octav e and what those names should be was one much discussed (though hardly pivotal) musical issue of the time. Hooke suggested a system of musical notation as an attempt to simplify and rationalize both reading and composing music. The division of the scale, a n issue closely touching on the tuning conundrum, pre occupied mathematicians and number calculations for the scale divisions. T hough acknowledging the necessity of some kind of temperament tuning for practical musical production, Hooke never went so far in musical theorizing as to offer any solution of his own devising; and he 88 Gouk, Music Science 214, 218. 89 Gouk, Music Science 201, 216.

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36 maintained that the true intervals were of just intonation (Pythagorean plus additional consonant intervals advocated by Zarlino ). 90 Newton Much greater even than Hooke, N ewton wrote that mast erwork of Western mathematical logic, Prinicipia mathematica (1687), but was loath to publi sh it. His friend Edmund Halley persuaded him to do so by paying for its publication under the auspic es of the Royal Society 91 Newton was a serious investigator of alchemy and considered his alchemical studies writing mostly concern his astrological and alchemical investigations and speculations; and his personal library included mostly books on these subjects and only a few on the new scientific philosophy. 92 The initial work on Prinicipia mathematica (1687), as discovery of the law of gravity was a product of his anno mirabilis the year Newton spent at home when Cambridge was closed for fear of the pl ague. Newton, though, saw both of th ese scientific mathematical accomplishments in terms of th eir value in celestial harmony; the Pythagorean musical ratios underlay his inverse square law. 93 scholia both the inverse square law and the law of gravity were adumbrated by the prisci theologi in 90 Gouk, Music Science 201. 91 The Royal Society, however, lacked the funds t o repay Halley, so recompensed him with multiple Historia piscium a lavishly illustrated non seller published by the Society the year before. In Ingenious Jardine, 36. 92 James, Music of the Spheres 160. 93 Gozza, Number to Sound 50.

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37 the mists of antiquity. 94 This consummate man of science and mathematics, the very epitome of seventeenth century brilliance, viewed his monumental intellectual creations as mere re interpretations of ancient encoded wisdom. Not surprisingly interest in music was based on mathematics. He developed his own system for the division of the scale, a task exercising theorists mightily because of its intimate connection with the tuning problem. Newton devised a chart of logarithmically calculated tem pered semitones that anti cipates almost precisely that in use today. 95 He seems more interested in the mathematical complexities and creating symmetry than in aural considerations; and he is anxious to construct a system of intervals, by theorizing tiny bui lding blocks of sound, that is closest to classic al just intonation. obsession with mystical number manipulation relating to ancient wisdom rather than a desire to derive some practical solution for the temperam ent problem facing practicing musicians. He used his acoustical work to inform his optical investigations, drawing an analogy (as others also did) between the musical scale and the color spectrum. 96 Newton, following Pythagoras, believed the cosmos to be st ructured by mathematics, evident in Principia and himself as an agent to recover ancient theological wisdom. His investigation into the harmonics of both music and color was part of his lifelong attempt to reveal the true basis of the harmony of the spher es, the 94 Walker, Studies 25. 95 Gouk, Music Science 233. 96 Gouk, Music Science 235, 237.

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38 truth of w hich had been encoded to hide it from the vulgar but symbolically and allegorically decipherable by a true philosopher such as Newton himself. The musical scale and the color spectrum relate to the actual harmony of the heavens, not the l iteral creation of tones by the motion of crystal spheres, but the entire mathematical edifice underlying the cosmos. 97 Newton saw himself, not as a discoverer of new truths about the working of the universe, but as one revealing its ancient, encoded wisdom. 98 97 Gouk, Music Science 251 254. 98 Peter Dear, Revolutionizing the Sciences: European Knowledge and Its Ambitions, 1500 1700 (Princeton, NJ: Princeton University Press, 2001), 169.

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39 CHAPTER 4. HUMANITY CREATING ITS OWN MEA NING Implic it w ith in the altered sources of authority and order is the notion that humans now have chosen to make do for themselves. The cosmos is delineated, humanity is in the ascendant, nature is knowable an d controllable a pyrrhic victory, exacted at t he cost of the severing of once vital connections: between nature and morality, meaning and spirit, authority, wresting power from a spiritually imbued cosmos to bring to earth as its own provenance, wraps the onus in the guise of a gift of increasing scientific hegemony. From now on, humankind itself must operate without reference to the harmony of the spheres. If there is to be harm ony, humanity must be both originator and guarantor. On its own in the cosmos, no longer p art of a great chain of being ensconced within a unique niche of the natural world, no longer dependent on a shared notion of cosmic harmony, rather relying on its own power to create and sustain, to order and deliver, to provide and satisfy humanity is the ultimate source for all its own physical, intellectual, and spiritual needs. One initially compelling metaphor maintains that the traditional religious ideology unde rlying the new theory of nature in the seventeenth century is the basso continuo supporting the status quo; new lyrics and melody are the changes in

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40 philosophy and religion that play over it. 99 But the basso continuo was not left unchanged, even if the moral religious ethos remained strong. Though not apparent early in the seventeenth century, the moral and the religious were destined to be only vestiges, however sincerely proclaimed, that eventually revealed their uselessness to the new natural philoso phy; the new basso continuo is the modern scientific enterprise: materialistic, radically divorced from religion, ideologically neutral. The source of morality, religion, and ideology no longer lies with the cosmos; humans now have the freedom, or bear the burden, of fashioning these anew for each individual and for society. It is a human made world, in much more than a merely technological sense. This new way of thinking about nature was part of a deep and wide shift within society political, philosophical and religious recognizing that humanity, without recourse to the immutable heavens, must now be in control of its own destiny, including the awful freedom to choose among diverse sources of authority and order. Th is new natural philosophy was not just a bout changing methodology. New epistemological shift. But in no sense was it a linear one. Renaissance era beliefs in analogies and correspondences continued to be cultura lly meaningful even as the scientific revolution proceeded apace. This contradictory, complex seismic shift can be viewed through artistic products as they reveal, though opaquely, 100 prevailing 99 Natural Order 101. 100 Sharpe, Remapping, 40.

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41 beliefs, concerns, and desires, expressing illusions as well as anxieties. 101 Reading cultural texts for ideological meaning is critical for the seventeenth century in particular because political thought and language did not even exist as a distinct, discrete level of discourse until the latter part of the century 102 and because the participants in the profound shift of cultural meanings in the seventeenth century were utterly unaware of the transformational enterprise of which they were a part. So the upheavals of the seventeenth century, far from being transparently exp ressed in 103 as writers agonized about their fear of disorder in the face of disintegrating certainties or, later in the century, more easily embraced the new epistemology identified by fragmentation of sources of authority and truth as old meanings and attachments mattered less and less. Music Central to That Change Music figures critically in this epic shift in having become, through evolution, hard wired into the human brain, a sou history. All know n societies have had music; it is intimately connected with the development of language dating to the beginning of our species 104 Music is central to what it means to be human ; so the musical conversation of the seventeenth century is even more heavily freighted with meaning than just one among any number of 101 Sharpe, Remapping 29. 102 Sharpe, Remapping 48. 103 Sharpe, Remapping 49. 104 Oliver Sacks Musico phi lia (New York: Random House, Inc., 2007), x.

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42 other cultural expressions as political statements. Music al writing however n arrowly focused is yet accessing a deep hu man reservoir of meaning of sources of order and authority. As humans assumed increasing autonom y, this epic shift is encoded in music thinking and writing. Changing Ideas of Nature in Music Writing That dividing line of seventeenth century English history the Civil War, was a cultural break in forcing the polity to confront the fact of fragmentation and loss of harmony; but it was not the cause or even the symptom of a sharp break in that belief in a unified and harmonic society. That had been eroding for some time, as evidenced in the temperament controversy in music. The realization that there was a problem with the intervals a s pronounced by Pythagoras was known by those who worked in music ; and with that realization came inevitable enormous cosmologica l implications: the harmony of the spheres was not as advertised. As musical theorists and practitioners grappled with the temperament problem, the out of sync intervals pointed to more questions, and questioning, about other accepted truths concerning the physical universe along with more mundane but pressing matters of politics and society. The new realizations and realities in society and philosophy meant that humankind was severing its spiritual ties to nature and cosmos, arrogating to itself the roles previously belonging to a sacralized universe, thus desacralizing those functions as they came within the realm of human created control and authority. Though

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43 musical treatise writers reveal an increasing sense of mastery as well as continuing anxiety about shifting cosmology through the century, the changes are highly contested and non linear. The Ro yal Society tended to attract men (a nd only men of course ) with a range of interests pertaining to t he new e xperimental philosophy, including music as a means of elucidating other ideas and occasionally musical topics per se M usical theorists were not stalw arts of the Society (though they occasionally had their papers on music theory topics presented for discus sion ), but rather focused their a ttention and writing on musical topics as ends in themselves ; and t here was much to contend with during the century when most modern music theory was developed, within the roiling context of what to do about tuning. While the major natural philosophers addressed music in a multi faceted, global se nse for a variety of aims, musical theorists were by contrast, singularly focused on music in a strictly theoretical sense in which it was central to the story of natural philosop hy in the seventeenth ce ntury Where the Royal Society elites articulated a broad range of interest in scientific topics related to the new philo sophy and occasionally includied music because of its connection to other kinds of knowledge, the musical theor ists pursued defined aims of developing music theory as they grappled with the tuning problem for polyphonic and instrumental music. The groups overl ap, of course; but this second were most known as musicians and musical theorists, rather than natural phil osophers wh o occasionally

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44 wrote about music. The musical structures developed by these theorists is nothing less 105 and so worthy of investigation. Though scholasticism was still being taught in the universities into the seventeenth century, neo Platonism dominated Renaissance thought and launched the seventeenth century, implicit in all institutions If new Platonism was concerned with 106 then the purpose of art was to demonstrat e the perfection in nature. As the foundation of beliefs about nature began shifting art became on e site of contention about the Platonic ideals, questioning a mo ral, meaningful, organic cosmos and the authority of the heavens in human affairs. Musical wr iters advocated a variety of solutions to musical theoretical problems, reflec ti ng and revealing the shifting bases of philosophical beliefs through their writing about music Questioning the neo Platonic notion of the harmony of the spheres a s a metaphor for the heavens as source of order and authority for humanity coincided with the changing notions of nature. As beliefs about nature dictate beliefs about music, so music was central to the questioning of old assumptions, though in mostly oblique ways. Mus ical writers did not set out to debate deep philosophical questions of meaning and authority; but their contentious writing was an active site for that debate, albeit unwittingly, and all the more so because the problem with Platonic intervals, the tuning problem, was of necessity so central to their discussion. 105 Sharpe, Remapping 94. 106 Sharpe, Remapping 448.

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45 Harmony of the spheres rife with correspondences in reflected realities of heaven and earth; an ordered and interconnected universe of hierarchy and beauty; an opaque, sacralized cosmos saturated wi th meaning and significance was Platonic ideas. 107 This universe was in sharp contrast to that which underlay the new philosophy. The latter demanded investigation and experiment. 108 Neo Platonism was at cross purposes to the new philosophy and lost its central role; it was not so much attacked as dismissed. With one foot still in the Renaissance, Bacon at the beginning of the century, had tried to recon cile the new philosophy with neo Platonism; and Newton at the end of the century, was still pre occupied with Platonic based pursuits. B ut by the end of the sevent eenth century, neo Platonism simply lost intellectual cache, out of joint with the times. century neo attempt to reinvest an already fatally secular cosmos with the sense of sacred 109 The description of the cosmos envisioned by neo P latonism was no longer seen as usefu l The Platonic id eal in music dictated that the perfect intervals were to be combined into compositions according to strict parameters based on consonances emanating from God and nature, to be discovered by man. The ancient foundation of music was number, as discovered by Pythagoras. Making good music meant choosing 107 Geneva, Astrology, 269. 108 Geneva, Astrology 271. 109 Geneva, Astrology 282.

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46 the right numbers, the correct intervals to create perfect consonances. 110 The Pythagoreans conceived of this precise, number ordered universe against the materialistic universe of Aristotelian natural philosophy. Aristotle himself wrote of the Pythagoreans that they believed mathematical principles, including musical ratios, to be the constituent elements of the whole of nature, the ultimate reality. Boethius (480 526) re iterated that Pythagoras discovered the ma thematical foundation of musical consonances in the perfect intervals. Mathematics is the foundation for harmony, spatial and musical. 111 Because this was such an all encompassing world view, it did not willingly depart the philosophical stage. Neo Platonism consequence for musical theory: from musical sound as number to vibration. Consonances were no longer based on simple numerical ratios but on vibration. The most concordant simultaneous ton es were th e ones whose vibrations coincided most frequently and regularly. Numbers were no longer the cause but only the representation of what was happening musically. 112 the imperfections in Platonic intervals in the late sixteenth century was the leading e dge of this dispassionate view of music informed by a mundane, knowable nature. Music in the modern world now is instrumental (both figuratively and literally) efficient, and harmonically calculated. 113 Equal temperament tuning is the ultimate 110 Gozza, Number to Sound 1. 111 Gozza, Number to Sound 2 4. 112 Jamie Kassler, Inner Music: Hooke and North on Internal Character (Madison, Teaneck: Fairleigh Dickinson University Press, 1995), 53. 113 Music Theory 20.

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47 rationalization of music; tuning thus rationalized for the purpose of fretted instruments playing in harmony has lost magic and divinity 114 and implies a nature also thus diminished. Pre modern music is highly rational in a literal sense based on divine ratios 115 Disenchantment of music means n o less than the untuning of the cosmos, the collapse of cosmic order. Modernity views the disenchantment of musical theory and the rationalization of tuning as obviou s and inevitable. B ut it was not so for sevent eenth century musical theorists or performers The latter had been making novel tuning accommodation s for instrumental and complex vocal music since the late Renaissance without confronting the philosophical contradiction with Pythagorean intervals. They simply did what they had to do to perform the music. This often meant mean tone tempering: diminishing a series of consecutive fifth intervals by a bit; but it worked well for only a few key s. These ersatz temperament solutions were not systematized and only more or less satisfactory, usually limiting the keys that a performer could play in. system of using more intervals than in the Pythagorean philosophy, still had the inconvenient problem because of using pure intervals, of music ending on a different pitch than the initial one : the basic prob lem of non tempered tuning the octave is not p reserved. Dutch philosopher Huygens contended that good singers (unaccompanied) will compensate for this instability by holding the original pitch in their heads in effect, creating their own tempered intervals. The 114 Max Weber, The Rational and Social Foundations of Music 115 Music Theory 22.

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48 trick, apparently, according to Huygens, was to get them to sing a piece quickly enough so as not to forget the original pitch. 116 Seventeenth century theorists, in engaging more directly with the philosophical issues of music theory, typically accepted the necessity of some kind of temperament adjustment while still holding on to ideals of Pythagorean perfection. The logical and the ideal then, co existed through the century, the latter giving way to the former only as neo Platonism and the idea of cosmologica l harmony lost intellectual space and became irrelevant space then taken up by the new experimental philosophy. The co existence of the pragmatic and the ideal was not always peaceful. Assumptions about nature inf ormed musical treati ses, which then became sites fo r contested notions of nature and the cosmo s, though the authors would not have perceived them as such. Probably the most noted and prolific treatise writer of the early centur y, most important treatise on music theory was an instruction manual for singers and plucked instrument players on the intricacies of improvising two, three, four, five, six, or more parts on a plainsong melody. It is far from being an exac t science. Modern music theory developed, haltingly and piecemeal, as a response to the increasing complexity of music beginning in the late Renaissance. 116 Walker, Studies, 112.

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49 his own treatise and 117 Morley is not shy about proclaiming his own theory. He directs the reader to xpresse any word 118 Going out of tune is unnatural because these are given by nature, not human artifi ce. Morley claims ancient sources for his musical writing, namely Plato for whom sciences 119 Morley also cites Boethius (fifth century Roman philosopher and mathematician whose five volume De Musica informed music scholarship into the other mathematical sciences 120 Morley cites these ancient sources to lend credibility to his own writing; but, despite his stridency about other musicians, he does not bre ak any new ground about the philosophy of music, 117 Thomas Morley, A plain a nd easie introduction to practicall musicke set downe in forme of a Curteous 118 Morley, A plain and easie part III, 177. 119 Morley, A plain and easie part III, 183 184. 120 Morley, A plain and easie part III, 184.

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50 content to simply cite ancient sources without challenge even while suggesting pragmatic temperament practices. Everyone seems to have his (virtually never her) own composition and performance rules, and Mor ley claims to organize the chaos He anticipates that many will read his book merely to find something for which to attack him by saying he is undercutting other practitioners with his own methods for making music; he proactively counter ooke will be so farre from the hinderance of anie, that by the contrarie, it will cause those whome they alledge to be thereby 121 possibly an allusion to temperament practices, although he do es not specify that. Anyone who guiftes of God should die in themselves, if they shoulde bee taken out of the 122 The tension is almost palpable, even from the distance of 400 years; and the intensity of feeling seems a symptom of the challenging of closely held beliefs that underlay developing musical theory Over the course of the century, the iron grip of these previously unquestioned beliefs about the nature of the cosmos as they impacted the practice of music loosened, not because anyone proclaimed it should be so but because a dogmatic adherence to Pythagorean perfectionism became inconvenient, an intellectual hanger on. But early in the century, the intensi ty of feeling expre ssed in 121 A plain and easie page unnumbered. 122 Morle y, A plain and easie Part II, 115.

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51 Thomas Ravenscroft in 1614, took on changes in practice and philosophy sick Age wherein we 123 He equates the discordant state of music with a commonweal which he sees in disarray. Complices censure me as t who did shine in the Firmament of our Art, and did first giue light to our vnderstanding with his with it a pity, since, if he did, others would surely follow because of his influence. 124 taking o divinely mandated precepts of music. 123 Thomas Ravenscroft (London: Edward Alide, 1614), opening Apologie. 124 Ravenscroft, discourse Apologie.

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52 125 Following the first section of the Apologie, a series s stance. Ravenscroft then concludes the Apologie by saying that concord and discord exist in all the arts, not just music; and he views himself as a messenger of peace to the chaotic state of music, to bring it back into concord and harmony with nature. Both Ravenscroft and Morley, then, are almost pleading for a return to basics, ematical i ntervals and harmony, even though they had to use some kind of tempering to perform music With their tradi tional stance roughly contemporaneous call to end speculation in music and just investigate it as any other facet of nature; but there is no evidence that they either one experimental advocacy. The f irst major theorist to accord with Bacon and to approach music experimentally rather than mystically was William Brouncker future Royal Society Compendium musica e 126 The introduction to the translation also included Br the scale with log arithms, the very anti Pythagorean notion o f dividing intervals into equal parts the firs t one to propose this kind of manipulation He wished to contest s are based on arithmetic and show that their true 125 Ravenscroft, discourse Apologie. 126 Still, Descartes relates in the Compendium that when drum skins of a wolf and a sheep are struck simultaneously, the sheepskin will remain silent for fear of the wolf.

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5 3 relationship is geometric. 127 Interestingly, though, he did not seem at all interested in solving the tuning problem; in fact, his calculations for various ways of dividing intervals do not preserve the octave, the whole point of tempered tuning. 128 Also in the introduction to the trans have competence in the entire range of subjects touching on music, including mathematics and magic and exper imental science, especially acoustics: 129 a Renaissance man and beyond! Coincidentally, i n t Compendium musicae Hugh Platt published The Jewel House of Art and Music and Nature It was an essay in the new philosophy on a mission to subdue, tame, and correct nature, wildness, and exotica 130 a popular and pragmatic sourcebook of hu man artifice to enhance nature. I t was a distinct departure from Morley and Ravenscroft and heralded increasing intellectual space for the practical over the mystical. That space opened up even more at the end of the c entury as philosophers focused on mathematical solutions to temp erament tuning and investigated consonances in the context of vibration science. Even in the last quarter of the century, thoug h, Thomas Salmon tenaciously clung to the notion that the true co nsonances are those perfect ones given by Pythagoras. intonation to duplicate the ethical effects of music that the ancients experienced. His 127 Gouk, Music Science 142. 128 Walker, Studies 117. 129 Gozza, Number to Sound 20 21. 130 Music Theory 40.

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54 Essay to the Advancement of Musick (1672) first argued his point passi onately. In 1688 he published A Proposal to Perform Musick, in Perfect and Mathematical Proportions, in which he famously proposed complex mechanical appendages to instruments to compensate for the tuning discrepancy while maintainin g just intonation; the system required interchangeable fingerboards and different frets for each string and was wildly impractical. He even gave up trying to explain the details and said that a mechanic would just have to figure it all out. 131 In Chapter 1 of A Proposal Salmon surveys the history of music. In ancient times, music had great power and flourished, then died during me dieval centuries. The present time is witness to a new glorious age of music with the potential of surpassing the ancients because of the advent of polyphony and many of these advances, one might conclude says Salmon, that nothing can be improved upon the present practice of music. 132 But wait; there i s something. The ancients made music world agrees that the more exact the proportions, the more excellent the music; a singer or instrument out of tune will ruin the best composition. So it is a great error of the present day that the beauty of g so many unp roportionate 131 Walker, Studies 115. 132 Salmon, A Proposal To Perform Musick, In Perfect and Mathematical Proportions (London: John Lawrence, 1688), Chapter 1, 2.

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55 133 Since the octave must be stable, some kind of tempering is in insists that the present day also. 134 In Chapter 3, Salmon launches into the explanation of his solution for the he exact tuning discrepancy, yer simply adjusts for each key; but of course, each fret must be tuned separately. But he has tested it and found it to be very convenient! Salmon does not presume to tell the se wi ll suffice to find the best mechanical solution possibly even better than the one Salmon himself has envisioned. 135 Salmon admits that in a few instance s, his system cannot correct the out of tuneness posal, Nature it self alter Nature, but to discover her Constitutions, and to give opportunity for the best Still, h e seems somewhat irked at nature for the imperfections in the supposedl y perfect Pythagore an intervals but concludes by re iterating that the proof is in the playing; his system indeed works. 136 Salmon straddles two epistemes: the ancients as the only true basis for music ma king and the 133 Salmon, Proposal Chapter 1, 3 4. 134 Salmon, Proposal, Chapter 2, 13. 135 Salmon, Proposal Chapter 3, 17 18. 136 Salmon Proposal Chapter 3, 23 28.

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56 recognition of ancient imperfection with a modern method to correct it. Like his contemporary Isaac Newton, Salmon identified with neo Platonism; and Newton A Proposal To Perform Musick, In Perfect and Mathematical Pro portions. Another major treatise writer at the end of the century, William Holder, manages to cite the ancients, offer pragmatic solutions for tuning, and add a religious devotional. 137 Chapter 2, where he defines intervals in slavish detail, using both the monochord 138 and pendulums to illustrate. pleasing to the ear, an aesthetic and natural rather than Pythagore an definition In explaining the way vibrations work, Holder says that playing two notes that are separated by only a half Motions, sucha Clatter and T 139 divide the scale in equal parts so to keep in tune, always keeping the diapason (octave) constant; the discrepancy between the perfect and tempered intervals according to Holder is approximately 1/53 of a diapason, which closely approximates 137 William Holder, A Treatise of the Natural Grounds and Principles of Harmony (London: J. Heptinstall, 1694). 138 The monochord was used in two ways: to explain perfect Pythagorean intervals and to explain ways of dividing the scale (or other intervals) into equal parts, usually as a solution to the tuning problem. 139 Holder, Treatise Chapter 3, 34.

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57 the actual irrational number. 140 This logarithmic system for equal temperament tuning is what Holder calls the 141 142 Holder is firm in sa ying possibly for intuitive reasons that only the approximations to the irrational numbers that precisely define the tuning discrepancy n themselves, should be used in creating equal temperament tuning. 143 In conclusion, he proposes some questions that bear further investigation: why do human voices at the same pitch sound so different ly from one another? why do the sounds of the respective instruments differ so from each other? why do some people not love music? (He suggests an answer to this one; there is a 144 Holder seems unquestioning about being in that epistemological space between neo Platonism and experimental philosophy, and includes a heartfelt dedication and thanksgiving to God. Francis North, in 1677, wrote an extended and innovative essay on acoustics, (possibly Hooke), noted in records of the Royal Society and credited with being the beginning of modern music philosophy by at least one music historian 145 By this time, acoustics and experimental investigation of sound were 140 Holder, Treatise Chapter 5, 67 84. 141 Holder, Treatise Chapter 6, 97. 142 Holder, Treatise Chapter 6, 116. 143 Holder, Treatise Chapter 9, 142. 144 Holder, Treatise Chapter 9, 152 153. 145 Kassler, Jamie C., with comments of I saac Newton, Roger North and in the Philosophical Transactions (Hampshire, England and Burlington, Vermont: Ashgate, 200 4).

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58 coming to dominate m usic discussion, with a continuing pre occupation with the criteria for concordant and discordant sound. Physical explanations were based on the coincidence theory of vibration North accepted this, but ranks consonances in a different order than Hobbes and Galileo, for example, whose ranking was based on a Pythagorea n arithmetical scheme; he ignores proportions in favor of sensory perception of synchronous pulses. 146 North was the first to investigate sou nd initiation and perception as well as the way the ear works as intermediary between these two processes, a novel empirical approach. 147 He suggests adding quarter tones to some notes as a way to preserve the octave and was the first to choose, from among the twelve Greek modes the two scales (major and minor) now in use 148 Still, a n aura of moral judgment in discussions of tonality and concord lingers : concordant sound is good, discordant sound is bad a vestige of moral framework of the cosmos. Only pleasing harmony is acceptable as a desired musical sound; discord is allowable only on the way to a pleasing concord, when the ear is assured that it will be speedily resolved. 149 Music unique capability to express human affect. 150 146 Kassler, Modern Philosophy 52. 147 Kassler, Modern Philosophy 77. 148 Kassler Modern Philosophy 79 81. 149 Kassler, Modern Philosophy 83. 150 Kassler Modern Philosophy 87.

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59 CHAPTER 5. THE NEW PHILOSOPHY: MUSIC AS SOURCE OF O RDER The waning of neo Platonism, as well as Aristotelian natural philosophy, was in n o way an indication of an increasing freedom fr om fear of disorder. Order anxiety was pervasive across classes and order widely perceived as fragile, a m ere veneer sublimating an archy. 151 From the first decades after 1500, all of Europe experienced a crisis of authority across all institutions and areas of human endeavor including the arts, brought on by the Reformation and a range of other social and political changes. 152 against each and that the problem of knowledge was the problem o f order, led him to reject the experimental philosophy Knowledge must not be tentative or contingent: absolute knowledge equaled social order. So for Hobbes, science must be premised on secure first causes, not in the business of investigating or debating them; and the failure of the new philosophy to proceed on a foundation of certain knowledge was no less than an invitation to civil war. 153 Hobbes notwithstanding, t he Civil War its elf was not about abandonin g order but rather overthrowing monarchial anarchy ; and after wards society seemed collectively appalled at what had been wrought regicide! and willing to become acquiescing moderates at the Restoration. As old certainties about cosmological order 151 Kevin Sharpe and Peter Lake, eds., Culture and Politics in Early Stuart Engla nd (Palo Alto: Stanford University Press, 1993), 11. 152 H. Floris Cohen, The Scientific Revolution: A Historiographical Inquiry (Chicago: University of Chicago Press, 1994), 210. 153 Cohen, Scientific Revolution 213 214.

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60 political upheaval, a n epistemological vacuum opened up ; and the new philosophy all about ruling and taming nature, filled tha t vacuum 154 The order offered by the New Science was correcting, subduing, and classifying nature with human artifice. I t was the right role at a critical time for the new philosophy. T ch aos 155 The sense of order was fundamentally shaken. This provided one impetus to put order 156 Early in the century, Bacon had insis ted that all errors in beliefs about nature should be banished Pseudodoxia Epidemica in five re issues, no less. Its organization is a metaphor for a newly ordered world h e was trying to help create. 157 It was a profound shift to this new source of order, one inevitably marked by ambivalence and befuddlement. Even as Browne repeatedly heaps scorn on both fundamentalist religious ideology and magical thinking, he unselfconscio usly subscribes to the class prejudices of the time in condemning the lower classes for being unenlightened in the new philosophy; and his false dichotomy of the enlightened upper class scientist versus the lower class ignoramus fails to appreciate the fact of elites practicing alchemy, oblivious to its contradiction with the new philosophy, and laborers and artisans well versed in 154 Clark and Rehding, Music Theory 40. 155 Campbell, Wonder, 4. 156 Campbell Wonder 6. 157 Campbell, Wonder, 86.

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61 understanding and absorbing the new ways of thinking about nature. 158 Browne is just one who is reacting to loss of the old or der by embracing the offer of a new one dogmatically, in his case. Rising from the ashes of the Civil War at a time, not coincidentally when England seemed anxious to leave all that disorder far behind, the conservative elites of the Royal Society approp riated the role of director of the new structure of order At a time of unrest, sources of meaning and authority were eagerly grasped. 159 Science was promoted by the elites as a means of social control since it is everywhere the same, not volatile and complex like politics O ne argument for the new philosophy 1667 History of the Royal Society 160 This is not an argument for social reform but rather for benefiting elites in promoting the political and social status quo and stability science for elites, not the wider population. Where Bacon had forcefully art iculated science for social utility for the material benefit of all the elites repurposed the scientific endeavor, taking ownership of it as a force for social order and control. 161 Identifying the New Science with social order, rather than subversive of it, propelled its acceptance; and for this reason, the break in order represented by the Civil War was the single most important event for the integration of the New Science. 162 Moderate reformers morphed into social conservatives the foundation for 158 Campbell, Wonder 97. 159 Jardine, Ingenious Pursuits, 39. 160 Margaret Jacob, The Cultural Meaning of the Scientific Revolution (New York: Alfred A. K nopf, 1988), 29 30. 161 Jacob, Cultural Meaning 38. 162 Jacob, Cultural Meaning 73.

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62 the Royal Society. 163 century, the science it had promoted became the foundation of a new epistemology. experimentation ; it was vehemently non partisan, scorning and eschewing anything 164 an ideal value free space for scholarly pursuits 165 was the goal, toward which results of observation and exp eriment could be marshaled. Philosophers 166 The ideal, if totally unrealistic, principle of an ordered, value free neutrality in the new philosophy was a powerful draw after the disastrous rivalries of the Civil War In service of that end, several New Science philosophers wanted a language transparent to all, a new lingua franca of normative scientific discourse, stri pped of all the richness, redundancy, and overtones of quotidian speech, signifying only and precisely the signified and reflecting a demystified nature. 167 Wilkins developed the Wilkins Universal Language, used by Hooke to announce his balance spring watch mechanism. 168 The universal language projects were dropped because of the impossible complexities involved. 169 Attempts to create a language somehow devoid 163 Jacob, Cultural Meaning 77 78. 164 Dear, Revolutionizi ng the Sciences, 118. 165 Henry Oldenburg (first secretary of Royal Society) in The Correspondence of Henry Oldenburg eds. A. R. Hall and M. B. Hall (Madison and London: University of Wisconsin Press, 1966), letter 2445. 166 Oldenburg, Correspondence Letter 2372. 167 Geneva, Astrology 273. 168 Jardine, Ingenious Pursuits 317. 169 Geneva, Astrology, 280 81.

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63 of human content inevitably foundered on the same inherent impossibility as that of value free science; but the belief of its possibility is evidence of the striving for defined order and authority in the wake of political rupture and philosophical dislocation. Acknowledging Diversity with Loss of Celestial Harmony As basic and long held political, religious, and philosophical assumptions became fodder for re examination, a necessar y corollary was the necessity of acknowledging diversity. Although this sea change had been going on since before the dawn of the seventeenth century, the Civil War forced recognition of a new state of affairs. England, at Restoration, did not return to pre war reality; the model of harmony and organic order could no longer be sustained. The religious and political conflict had come into glaring focus and could not be manag ed with a hegemonic ideal of unity and homogeneity. 170 Tolerance for differing views, accommodation of di v ersity was the radically new challenge of the seventeenth century as it emerged into modernity The first manifestation of the breakdown of unity the Protestant Reformation meant that s ources of communal order shifted from public ritual and consensus to individual godliness; protestant spirituality was experienced individually rather than communally, symptomatic of the dismantling of the narrative of u nity as a useful way to describe society. The fragmentation of religious belief presaged and hastened 170 Crisis in Europe 1560 1660 ed. Trevor Aston, (New York: Basic Books, Inc., 1963), 335.

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64 accommodation of political and philosophical fragmentation. In this way, the midwife for the future, 171 a future defined by secularism of the modern state in Western society. The abandonment of unity was centered in the tumult within natural philosophy. Much more than merely the seventeenth century term for science, natural philosophy was a more comprehensive belief system about cosmological structure and meaning, the character of matter and of cause, and the proper basis for natural knowledge not conformable to any single modern discipline. Competing claims of Aristotelian based Scholasticism, neo Platonism, and the new mec hanical philosophy characterize the entire s eventeenth century; and interpreting the changes as a simple case of natural philosophy sinking into oblivion as science brilliantly ascends is a profoundly misreading of the cultural significance of all of the v oices in the conversation of the seventeenth century 172 The competing sources of authority the fragmentation itself, are the story of budding modernity. In music, the waning of the ideal of unity meant the abandonment of the absolute: intervals are not qui te perfect and consonance is not an absolute quality but one of de gree Rather than based on perfect Pythagorean intervals, consonance came to be recognized as the coincidences of the termination of frequency cycles between two st rings. Frequency ratios are not placed into discrete categories of consonance or 171 Patrick Collinson, The Birthpangs of Protestant England: Religious and Cultural Change in the Sixt eenth and Seventee nth Centuries, 172 Anstey and Schuster, Science o f Nature, 1 2.

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65 non consonance but rather are on a continuum of consonance. 173 So the idea of concord changed from mystical numbers as the foundation to coincidence of sound vibration. The mos t concordant simultaneous ton es are ones that coincide most regularly and frequently; infrequent or random tones are discordant. Numbers are no longer the cause, but merely the representation of sound. Concord and discord are not contradictory qualities bu t part of a continuum. 174 This abandonment of the absolute quality of consonance is both manifestation of and metaphor for the changes wrought in seventeenth century natural philosophy. Continuing Religiosity With Philosophical Changes The single characteri stic shared among virtually all writers, philosop hers and theorists alike is a profound religiosity agenda for the new philosophy to better the lot of hu preoccupation with ancient religious revelation, this century was marked b y the primacy of religion. Even as the seeds of fragmentation, diversity and thus secularism were sown by the Protestant Reformation, individual writers consistently and clearly articulated their religious commitment s This remains true even as ideas of nature and the cosmos, of order and authority, were being renegotiated, as seen in the musical treatises. 173 Seventeenth Century Science and the Arts, ed. Hedley Howell Rhys (Princeton, NJ: Pr inceton University Press, 1961), 109. 174 Kassler, Inner Music, 53.

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66 Still, this renegotiation in areas touching on religion created a cloud of suspicion of atheism over the new philo sophy The College of Physicians, fe eling their status quo threatened by the new philosophy, hired an agitator to attack scientists of the Royal Society as being anti religious and so undermining the social order and the common understanding of God. A ccusations of irreligiosity, albeit by a paid rabble rouser, could be taken seriously The crux of the atta ck was that the mechanical God of the new philosophers is not omnipotent and so can no longer work miracles. 175 Suspicion about the new philosophy was not limited to the uninformed. After the Restoration, when the conservative elite dominated and busily institutionalized the new science, seemingly contradictory claim s for a clockmaker God Who created the cosmos and stepped away to let it run according to physical laws on one hand, while yet being interested in the minutiae of human existence on the other 176 Some historians since have also read the new cynically crafted to appease a do ubting public. 177 This reading, though, belies a historicist understanding of this very religious century; and part of the answer for the conundrum of continuing sincere religious belief among the new philosophers rests on t wo notions of God uneasily co existing through Church history and brought into relief in this century of uphe av al 175 Francis Oakley, Omnipotence, Covenant, and Order (Ithaca: Cornell University Press, 1984). 176 His scorn was particularly directed at Newton and became intertwined with their bitter rivalry over which of the two was the first inventor of the calculus. 177 Oakley, Omnipotence 73.

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67 The two notions of God refer to the dual powers of God, absolute and ordinary, vying for primacy through the Middle Ages, Renaissance, and i nto the Platonism, which inhered in early Christian theology and are associated with the Great Chain of Be ing; God is not constrained by anything and is able and free to even susp powers are philosophically aligned with Aristotle and became the dominant notion of God with the influx of his writings in the twelfth century. s ord inary powers are those of the God Who created a lawful cosmos and adheres to those laws; as such, He is knowable and transparent to rational investigation. 178 Scholasticism which enshrined this latter notion of God dominated Church teaching well into the seventeenth century, notwithstanding an attack by fourteenth century nominalists who maintained that God is inscrutable and not amenable to rationalist analysis philosophical adumbration of the seventeenth century s cientific revolution. 179 The elite, post Restoration new philosophers of the seventeenth century, then, tapped into both notions of God, the dual powers of God, in claiming both a Creator God of a lawful cosmos as well as a personal, unconstrained God Who c ould transcend these laws if he wishe d (which H e has promised by covenant not to do). This was their stance against charges of atheism, a more embracing, not limiting, 178 The famous condemnation of Aristotle by the Bishop of Paris in 1277 w as an attack on the Aristotelian idea that God could in any way be constrained, including by divinely created physical laws. The Bishop lost that battle. 179 Oakley, Omnipotence 81.

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68 notion of God. Understanding t hese religious subtleties und ermines the theologically uninformed interpretation of seventeenth century protestations of religiosity as either nav e te or deliberate obfuscation. One cannot know the minds of individual s of course; but certainly the prevailing sentiment of the century was one of sincere religio sity. 180 The religiosity permeated all of society an d was not limited to some narrow phi losophical religious agenda of the elites. Musical treatise writers credited religious motivation and inspiration for their efforts or simply alluded to God in incidental ways throughout their treatises. In his 1588 treatise on vocal and instrumental music John Case 181 The character of these allusions subtly shifted, n ot surprisingly, through the century. Early on, references to the Divine actually embraced God, the cosmos, and heavenly harmony. Late in the century, religion became disengaged from natural philosophy as the new, morally neutral exp erimental science moved into ra ther than incidental, forceful re articulation s of that which seems threat ened because no longer philosophically necessary Religion though still vitally important to individual s, necessarily engage d differently with an emerging philosophy that was not dependent on moral meaning in 180 Earlier in the century, before the conservative, moderate elites dominate d the New Science and institutionalized it with the establishment of the Royal Society, radical Protestant reformers and new scientists had formed a pragmatic alliance, united primarily in their opposition to the Roman Church, though for different reasons. Puritan theological rigidity caused the breakdown of this tenuous alliance well before the Restoration. 181 Music Theory 30.

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69 the universe; and this is apparent in music treatises. In his 1694 musical treatise scientifically analyzing the division of the scale, William Holder still proclaims the divine in music. Following a detailed discussion of intervals and tuning, Holden goes on to state that Nature of Harmony and are more than we can hope to fully understand although the search for answers must go 182 Toward the e nd of the century, St. Cecelia morphed into the patron saint of music, not her original role, as she became 183 As nature lost its cosmological significance, it became increasingly identified with religion This natural theology was in ascendance compatible with the new experimental philosophy. Thomas Mace and Nicholas Brady both wrote, during the last quarter of the seventeenth century, about the importance of music in p raising God. Each treatise has an anxiously persuasive tone, as if need ing to justify its stance. Mace, a cleric at Cambridge University, created a widely used and respected instructional manual for singing correctly and in tune in church, so as to glorify God. Interestingl y, he dedicates it especially to 184 who might not be initially friendly to the idea of music in church; Mace is on a mission to convince them 182 Holder, Treatise, 54 55. 183 Music Theory 59. 184 Thomas Mace, civil, that has ever been known to have been in the world (London: T. Ratcliffe and N. Thompson, 1676), frontispiece

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70 otherwise. The first part instructs congregations of parochial churches how to sing psalm s well, or do not bother to sing them at all, and suggests how cathedral music 185 I n rhyming verse, Mace insists that clerics must lead by example, learning music well to set a high musical standard as a model for their congregations. It is Acchord)/ In Singing Psalms, with Grace unto the Lord./ Sed sine Arte, That cannot 186 Ancient King David, psalm singer and harp player, is the shining example of musical leadership out in the world rather than cloistered with books, able even to fashion his own musical ins Mace acknowledges he is speaking boldly, but knows that advocating for music in church is rue D octrine. y 187 Music is divinely mysterious, as will be obvious to anyone who earne stly studies it, capable of stirring great religious ecstasy. Mace goes on to vilify, with much name calling, those who criticize his argument from a stance of ignorance 185 Mace, frontispiece. 186 Mace, first part, page unnumbered. 187 Mace, first part, page unnumbered.

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71 He considers it a pity that so fe powerful Souls and Spirits of Men Divinely 188 ncing t he worship experience. Mace feels impelled to provide instruction in good singing to parochial churches to counteract the shocking st ate of musicianship among non cathedral congregations 189 Very interestingly, he claims that singing in tune unaccompanied is a virtual impossibility, even for a singer with a discerning ear; instrumental acco mpaniment is required to keep both a solo singer and an entire congregation of music must be enhanced by human artifice; and the organ is the best choice. Even an indifferent singer would be hard pressed to sing out of tune with an organ guiding the musical way. 190 And Mace offers proof, real proof, of the efficacy of tuneful singing During a 1644 siege by three armies at York Cathedral which was filled with people, the cannon shot was unable to angelic, tuneful psalm singing. 191 In his discussion of cathedral music, following the parochial music section, Mace attacks more directly the dissenters who eschew music in church. He says that England has attained the highest level of art in church music composition; and to 188 Mace, first part, page unnumbered. 189 Mace Chap. II, page unnumbered. 190 Mace, Chap. V, 9. 191 Mace , Chap. V, 19 20.

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72 refu se to use this divine resource for worship is to profane it. He then offers a prayer Discording Christians, so that they may have a Right Discerning of the True Worship and Se acceptable to God. 192 But Mace has only begun his diatribe against music eschewing proceeds with a most vicious 193 Apparently, the bitterness of the banning of church music during the interregnum is little abated at this point. The dissension and disunity for which there is not yet a political language are yet capable of being expressed in art. The bulk of the treatise, nearly 250 pages, instructs singers and instrumentalists in the fine art of making tunefu l music for the purpose of right worship. Mace concludes with a ge neral discussion about concord and discord that almost reads as if written in the first part of the century because it emphasizes the mystical character of music, something far more than the sum of the musical parts. He reverts to the old standby of the stretched string to begin an explanation of intervals but, curiously, confines hims elf to explanation of the octave, repeatedly created by es. (Perhaps Mace thought that any complicated discussion of the tuning problem would distract from his core message.) love and hate, light and 192 Mace, Ch. V, 29. 193 Mace,

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73 dark, good and evil eements, and 194 Music car ries moral weight. But Mace also demonstrates a more modern approach in moving beyond intervals to focus on chords as well especially the 1 3 5 chord, particularly harmonic because reflecting the Holy Trinity. The concordance of three voices singing the tones simultaneously is much more pleasing than hearing them sounded separately, the 195 Mace concludes by re ite rating than anyone who tries out his system of learning to make g mystical and Beastical Sin 196 He cannot resist a short adjunct section about the mystical power of Significantly, and Powerfully fit for Divine, and Contemplative Good Christians, than 197 Because of its spiritual and emotional power, musi 198 M usic retains mystical power; but it is located squarely within the divine religious experience, with no connection to neo Platonic mysticism or Pythagorean perfect intervals. Even in his discussion of the stretched string to explain the wonder of the octave, Mace avoids any mention o f 194 Mace, 265. 195 Mace, 267. 196 Mace, 268. 197 Mace, 270. 198 Mace, 272.

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74 spiritual power. Even later in the century, Nicholas Brady cleric and librettist for Henry Purcell 199 Brady begins b y cataloging events in the Bible celebrated by heavenly music seeming to belabor the point as he cites Bible verses focusing on the centrality of music on numerous spiritually notable occasions. 200 He concludes from this that music, both vocal and instrumen tal, is 201 Reli Delights. Those who would Mo roseness and by banning music from worship have done religion a great disservice; and it w ould be unnecessary to make that 202 God Himself enjoins man to make m some is no reason to eschew it altogether. If that argument for its banning from 199 Nicholas Brady, Church musick vindicated : ry feast of the Lovers of music (London: Printed for Joseph Wilde, 1697). 200 Brady, Chur ch musick 2 5. 201 Brady, Church musick 5 6. 202 Brady, Church musick 8.

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75 religious use were reasonable, it would follow that poetry should also be banned from religious use because of the d ebauchery of some verses. Music naturally directs us to 203 Alluding to recent political discord, a shattering of the peace now mended, Brady offers a 204 Brady concludes by saying he is sorry fo unhappy Aversion to Divine Harmony, renders them unlike to the Saints and Blessed 205 Like Mace, Brady makes mention of neither Plato nor Pythagoras in his urgent advocacy of instrumental and vocal music in church. He speaks lovingly and passionately about the mystical and divine properties of music, capable of moving men to heights of joy and wonder, eliciting from them the best that God has put into humanity. None of this has to do with anci ent wisdom, though; it is all about the Christian religious experience. The divinity of music is not to be found in number mysticism but in its power to connect humans to the divine presence through this divinely ordained art 203 Brady, Church musick 10 12. 204 Brady, Church musick 17. 205 Brady, Church musick 23.

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76 CHAPTER 6. CONCLUSION Music writing offers a window to illuminate the changes wrought over the course of the tumultuous seventeenth century concerning sources of order and authority. The fragmentation across political and religious institutions was mirrored in profound changes in natural philosophy. As the narrative of the harmony of the spheres lost intellectual space to New Science, treatises and other music writing became site s for contested ideas about shifting intellectual spaces. Religion seems to be a constant; writers th roughout the century express deep and sincere religious sentiments which are not apparently diminished by the new natural philosophy or the fragmentation in religion itself. The constancy is an illusion, though. Even if individual sentiment did not wane, t he way in which religion engaged with philosophy changed fundamentally. When the harmony of the spheres was dominant, a unified vision of the cosmos with a place for everything (and everyone) and everything in its place, religion was part of that unified s cheme; it shared cosmological space with natural philosophy. But as ideas of nature drastically changed and the new experimental philosophy came into ascendance, there was no longer any intellectual space for r eligi on. Religion became extraneous: a persona l choice rather than a philosophical necessity The urgent sounding re articulation of the importance of church music after the Restoration attests to a growing, if still unconscious, nervousness about the cultural role for religion when it no longer matte red to the new philosophy.

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77 When the cosmos was tuned to the music of the spheres, order inhered throughout the universe, a given of human existence. But when the cosmic music was silenced, order was no longer to be found in the cosmos. Humankind was now un encumbered free from cosmic control and the certainly that accompanied it. Order must now be imposed by a newly autonomous humankind. Music treatises illuminate that highly contested process, fraught as it was with such great cosmological significance revealing a deep level of discomfort as previously unquestioned certainties are now fodder for debate. The level of vitriol is astounding as debates were fought bitterly over issues ranging from the inconsequential whether or not to label notes with syllab le names to the central problem of the Platonic foundation of intervals The bitterness and deep animosity among treatise write rs seems to encode the fear of the new reality of a desacralized cosmos The tuning problem, that the Platonic intervals were no t perfect at all for performing polyphonic and instrumental music along with the corollary issues of the nature of consonance and the proper division of the scale was the most critical issue for the music world in the seventeenth century and was met by a v ariety of responses that shed light on the way epistemological change occurred over the course of the seventeenth century. The tuning problem could not reasonably be ignored ; musical performance demanded some kind of re solution. For some, it was the elepha nt in the room. They worked around it limiting the music they played or the range of music limiting the keys they used to perform music, making on the spot adjustments to instruments or

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78 individual tuning of instruments for specific pieces but not confront ing, metaphysically or technologically, the core issue of the imperfection of the Platonic intervals. Of the other perhaps more philosophically inclined thinkers and writers on music, some may have been excited about the new experimental philosophy and not sorry to give up cosmological certainty for the prize of new knowledge of nature and Bacon, though not offering comment about tunin g specifically, forcefully eschewed musical mysticism. Hooke seemed unabashed by the metaphysical consequences of tempered sense of reality was founded on Platonic mysticis m, but he also joined in the musical acoustics, consonance, and the scale. Most of the both philosophically and musically inclined were more mixed in their confrontations with the tuning issue. They developed or subscribed to new tuning paradigms while convincing themselves that somehow, Platonic certainty still inhered in the cosmos. This was Thomas Salmon, who invented ludicrously unwieldy mechanical contraptions to fit on instru ments so that musicians could still use just intonation. Others saw various methods of dividing the scale into equal pieces to develop a system of tempered tuning not as abandoning but rather redefining cosmic harmony. The range of responses is witness to the shifting and re alignment of intellectual space in the seventeenth century.

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79 Because of this metaphysical and intellectual jostling, neo Platonism and the harmony of the spheres, cosmological certainty and a unified narrative of religious, political, an d cultural reality all were eventually squeezed out of meaningful existence. But it wa s not because anyone made it so; and it was not deliberate, systematic, or linear. Certainly there was never a conference called to discuss the tuning problem and come up with a workab le solution or fashion a compromise. Even the kind of profound epistemological change such as occurred in the seventeenth century is piecemeal, unconscious, at times retrograde. There is no zero sum game of experimental philosophy or tempered tuning advancing and taking over the old cosmological thinking. Music lost cosmological significance, not through willful advocacy, but because it ceased to be an important way to view the cosmos. No one in the seventeenth century, even the brightest and most prescient, could have surveyed the sweep of the century and announced the epistemological shif t There is no announcer, neither declarer nor decider. The paradox of historical change is that it occurs only through sentient, willful actors; yet what is wrought is unforeseen, little understood, and la rgely unintended, always prey to some level of historical contingency and written in the passive voice. People through the century placed a host of meanings on the political, religious, and philosophical upheaval ; and change happened, fundamentally and permanently.

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80 WORKS CITED Anstey, Peter B and John A. Schuster. The Science of Nature in the Seventee nth Century: Patterns of Change in Early Modern Natural Philosophy New York: Springer, 2005. and Schuster, eds. Aston, T. H. Crisis in Europe, 1560 1660 New York: Basic Books, 1965. hidden world in seventeenth century England. In Music Theory and Natural Order from the Renaissance to the Early Twentieth Century edited by Suzannah Clark and A lexander Rehding. New York: Cambridge University Press, 2001. Aveni, Anthony F. Behind the Crystal B all : Magic, Science, and the Occult From Antiquity T hrough the New Age New York: Times Books, 1996. Bacon, Francis, and Richard Foster Jones. Essays, Advan cement of Learning, New Atlantis and Other P ieces New York: Odyssey Press, 1937. Barnes, Barry, and Steven Shapin. Natural Order: Historical Studies of Scientific C ulture Thousand Oaks: SAGE Publications, 1979. Brady, Nicholas. Church musick vindicated a sermon preach'd at St. Bride's church, on Monday, November 22, 1697, being St. Caecilia's day, the anniversary feast of the Lovers of musick London: Printed for Joseph Wilde, 1697. Campbell, Mary B.. Wonder and Science: Imagining Worlds in Early M odern E urope Ithaca: Cornell University Press, 1999. Music Theory eds. Clark and Rehding. Clark, Suzannah, and Alexander Rehding. Music Theory and Natural O rder from the Renaissa nce to the Early Twentieth C entury New York: Cambridge University Press, 2001. Cohen, H. Floris. The Scientific Revolution: A Historiographical Inquiry Chicago: University of Chicago Press, 1994. Collinson, Patrick. The B ir thpangs of Protestant England: Religio us and Cultural Change in the Sixteenth and Seventeenth C enturies New York: Macmillan,